5 ZADACI ORGANIZACIJA...6. У периоду од два месеца или 46 радних дана треба обавити превоз шећерне репе и то 46800 m3

ЗАДАЦИ ЗА ТАКМИЧЕЊЕ ИЗ ОРГАНИЗАЦИЈЕ ПРЕВОЗА 1 Из фабрике мотора у месту А потребно је у току 183 дана односно 160 радних дана транспортовати 15 000 комада мотора у фабрику аутомобила у место C У повратку се транспортују алуминијумски профили и блокови из места B у место А Укупна количина блокова је 8600 t Транспорт се врши равномерно у току радних дана На површину товарног сандука може да стане 6 мотора припремљених за транспорт Тежина мотора је 600 кг носивост камиона је 3 t Време утовара и истовара једног мотора је 12 а утовар алуминијумских блокова и профила траје као и истовар 10 минута по возилу Остали подаци су γ2=08 Vs=40kmh Hr=8h tos= 05h Израчунати Ar= Uuk=

C G

40km 2кm

B 80km A

Поставка Решење

htoshkmVs

voztitumotui

tqhH

tkgGtQukmotoraMuk

danaDdanaD

r

m

r

i

5040

80min10

min123

860600

860015000

160185

2

22

1

2

===

===

==

====

==

γ

τ

htitutuihnuituihtuituitui

hVsKt

tw

htostuitwto

obrttoVsK

HrZ

tGMukQuk

vozilaDZq

QukA

o

o

n

o

m

ror

330min2010101min60512

3313301

64012022

837503316

101183740

2282

90006015000

19160113

9000

222

11

21

1

1

1

11

==+=+===sdot=sdot=

=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=minus

=

=sdot=sdot=

=sdotsdotsdot

=sdotsdotsdot

=

τ

γ

vozDZq

QukA

motGqn

ror

m

2239221601803

8600

56031

2

22

1

asymp=sdotsdotsdot

=sdotsdotsdot

=

=sdot

=sdot

=

γ

γ

n=5 мот може максимално да стане у возило

tkmKtQukKtQukUuk 176800080860012090002211 =sdot+sdot=sdot+sdot=

vozAAAA rrrr 22212 ==rArrgt

2 Из фабрике мотора у месту А потребно је у току 195 дана односно 180 радних дана транспортовати 18 000 комада мотора у фабрику аутомобила у место C У повратку се транспортују алуминијумски профили и блокови из места B у место А Укупна количина блокова је 7600 t Транспорт се врши равномерно у току радних дана На површину товарног сандука може да стане 7 мотора припремљених за транспорт Тежина мотора је 800 кг носивост камиона је 5 t Време утовара и истовара једног мотора је 10 а утовар алуминијумских блокова и профила траје као и истовар 25 минута по возилу Остали подаци су γ2=09 Vs=80kmh Hr=15h tos= 01h Израчунати Ar= Uuk=

C G

30km 6 km

B 70km A


htoshkmVs

voztitumotui

tqhH

tkgGtQukmotoraMuk

danaDdanaD

r

m

r

i

1080

90min25

min105

1580800

760018000

180195

2

22

1

2

===

===

==

====

==

γ

τ


hVsKttw

htostuitwto

obrtatoVsK

HrZ

tGMukQuk

vozilaDZq

QukA

o

o

n

o

m

ror

830min5025251min60610

3318301

528010022

4341083152

335343480

62152

144008018000

5180315

14400

222

11

21

1

1

1

11

==+=+===sdot=sdot=

=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=minus

=

=sdot=sdot=

=sdotsdotsdot

=sdotsdotsdot

=

τ

γ

vozDZq

QukA

motGqn

ror

m

31331803905

7600

62568051

2

22

1

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdot

=sdot

=

γ

γ





C G

50km 4km

B 90km A


htoshkmVs

voztitumotui

tqhH

tkgGtQukmotoraMuk

danaDdanaD

r

m

r

i

15060

80min15

min206

1270700

450020000

150200

2

22

1

2

===

===

==

====

==

γ

τ

htitutuihnuitui

htuituitui

hVsKttw

htostuitwto

obrtatoVsK

HrZ

tGMukQuk

vozilaDZq

QukA

o

o

n

o

m

ror

50min30151562min160820

135062

646014022

8571501364

2891857

604215

2

140007020000

8787150216

14000

222

11

21

1

1

1

11

==+=+===sdot=sdot=

=+=+=

=sdot

==

=++=++=

asymp=

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=minus

=

=sdot=sdot=

asymp=sdotsdotsdot

=sdotsdotsdot

=

τ

γ

vozDZq

QukA

motGqn

ror

m

31331502806

4500

85787061

2

22

1

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdot

=sdot

=

γ

γ





C G

30km 7km

B 55km A


htoshkmVs

voztitumotui

tqhH

tkgGtQukmotoraMuk

danaDdanaD

r

m

r

i

450

930min14

min404

1290900

560014000

200220

2

22

1

2

===

===

==

====

==

γ

τ

htitutuihnuitui

htuituitui

hVsKttw

htostuitwto

obrttoVsK

HrZ

tGMukQuk

vozilaDZq

QukA

o

o

n

o

m

ror

470min281414672min160440

34062

4350

85224104343

1111541050

72122

126009014000

16200114

12600

222

11

21

1

1

1

11

==+=+===sdot=sdot=

=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=minus

=

=sdot=sdot=

=sdotsdotsdot

=sdotsdotsdot

=

τ

γ

vozDZq

QukA

motGqn

ror

m

853720029304

5600

44449041

2

22

1

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdot

=sdot

=

γ

γ





C G

45km 8km

B 90km A


htoshkmVs

voztitumotui

tqhH

tkgGtQukmotoraMuk

danaDdanaD

r

m

r

i

145

950min42

min133

1690900

965016000

150200

2

22

1

2

===

===

==

====

==

γ

τ


hVsKttw

htostuitwto

obrtatoVsK

HrZ

tGMukQuk

vozilaDZq

QukA

o

o

n

o

m

ror

41min844242650min39313

05241650

64513522

05910526

2059

458216

2

144009016000

16150213

14400

222

11

21

1

1

1

11

==+=+===sdot=sdot=

=+=+=

=sdot

==

=++=++=

=

sdotminus

=minus

=

=sdot=sdot=

=sdotsdotsdot

=sdotsdotsdot

=

τ

γ

vozDZq

QukA

motGqn

ror

m

11281115029503

9650

3339031

2

22

1

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdot

=sdot

=

γ

γ




6 У периоду од два месеца или 46 радних дана треба обавити превоз шећерне репе и то 46800 m3 из места А у место B удаљено 80 км камионима са полуприколицом носивости 26 t Димензија товарног сандука A∙B∙C=50∙24∙12 m и полуприколице Arsquo∙Brsquo∙Crsquo=75∙24∙12 m специфична запреминска тежина шећерне репе је 065 tm3 Време утовара и истовара је 2 mint Vs=30 kmh Hr=16 h У повратку се вози црни лук чија је запреминска тежина 07 tm3 Vreme utovara i istovara u obrtu je tui2=2h Коефицијент техничке исправности возног парка је 08 a коефицијент искоришћења исправног возног парка је 1 Израчунати Ar Ai ρ δ β Uuk као и пуну и радну производност возног парка

Решење

Поставка A Kt1= 80km B

Di=60dana

1802

7016

30min2

650214257

21420526

8046800

46

2

32

1

31

1

3

=prime===

====

sdotsdot=primesdotprimesdotprimesdotsdot=sdotsdot

==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituituituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

780min846902627822780

33530

8022118782335

2971118

16

141144629026

304203042065046800

111

21

1

1

11

11

==sdotsdot=sdotsdot==+=+=

=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111

1sdotprimesdotprimesdotprime+sdotsdotsdot

=sdot+sdot

=γ 9026

650214257650214205=

sdotsdotsdot+sdotsdotsdot=

vozilaArAi 1851780

14asymp===

α 80180 =sdot=primesdot= ααα t

tDrArZoqQuktQukQukQuk

tkmKtQukUuk

363248346142970263662903363248330420

85032268807264966

22

21

1

=sdotsdotsdotsdot=sdotsdotsdotsdot==+=+=

=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 97026

7021425770214205=


660118335

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

38488161446

85032268

161614463662903

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

15194601824

8503226824

4326018243662903

24

=sdotsdot

==

=sdotsdot

==

6702416

24===

Hrρ

7 У периоду од 50дана или 36 радних дана треба обавити превоз робе и то 36800 m3 из места А у место B удаљено 60 км камионима са полуприколицом носивости 36 t Димензија товарног сандука A∙B∙C=50∙22∙15 m и полуприколице Arsquo∙Brsquo∙Crsquo=65∙22∙15 m специфична запреминска тежина те робе је 075 tm3 Време утовара и истовара је 3 mint Vs=40 kmh Hr=14 h У повратку се вози друга роба чија је запреминска тежина 09 tm3 Време утовара и истовара je tui2=3h Коефицијент техничке исправности возног парка је 06 a коефицијент искоришћења исправног возног парка је 1 Израчунати Ar Ai ρ δ β Uuk као и пуну и радну производност возног парка

Решење


Di=50dana

1603

9014

40min3

750512256

51220536

6036800

36

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

421min32857903634243421

340

60224274243

2881427

14

13471336279036

276002760075036800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 79036

750512256750512205=


vozilaArAi 22662160

13asymp===



tkmKtQukUuk

243167436132940362459274243167427600

43556454602459274

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 94026

9051225690512205=


404273

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

80542141336

43556454

0491413362459274

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

71134502224

4355645424

2525022242459274

24

=sdotsdot

==

=sdotsdot

==

5802414

24===

Hrρ


Решење


Di=90dana

1903

8016

40min8

440512207

51220532

4016800

72

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

32min2413854032835332

240

402237352

219237

16

397272254032

7392739244016800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 54032

440512207440512205=


vozilaArAi 333390

3asymp===



tkmKtQukUuk

7613685723299032762107776136857392

4843110407621077

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 99032

8051220780512205=


27037

2===

totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

9624316372

4843110

16163727621077

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

6416272324

484311024

074723247621077

24

=sdotsdot

==

=sdotsdot

==

6702416

24===

Hrρ

9 У периоду од 30 дана или 24 радних дана треба обавити превоз робе и то 23800 m3 из места А у место B удаљено 400 км камионима са полуприколицом носивости 33 t Димензија товарног сандука A∙B∙C=80∙242∙15 m и полуприколице Arsquo∙Brsquo∙Crsquo=75∙242∙15 m специфична запреминска тежина те робе је 055 tm3 Време утовара и истовара је 12 mint Vs=30 kmh Hr=12 h У повратку се вози друга роба чија је запреминска тежина 04 tm3 Време утовара и истовара je tui2=4h Коефицијент техничке исправности возног парка је 09 a коефицијент искоришћења исправног возног парка је 09 Израчунати Ar Ai ρ δ β Uuk као и пуну и радну производност возног парка

Решење


Di=30dana

90904

4012

30min12

5505142257

514220833

40023800

24

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoDrHrZ

vozilaZq

QukAA

tgkVQuk

o

orr

26min243729403312210426

67263040022

87362106726

881787362412

537552894033

130901309055023800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 94033

55051422575505142208=


vozilaArAi 664365810

53asymp===


tArZoqQuktQukQukQuk

tkmKtQukUuk

56951453868033562260456951413090

523600040013090

22

21

1

=sdotsdotsdot=sdotsdotsdot==+=+=

=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 68033

405142257405142208=


72087366726

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

03343125324

5236000

4811253245622604

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

73154306624

523600024

6703066245622604

24

=sdotsdot

==

=sdotsdot

==

502412

24===

Hrρ

10 У периоду који има 72 дана потребно је организовати превоз 7200 t робе из места А у место Б удаљено 60 кm Транспорт се врши у равномерним дневним количинама а број радних дана је 60 Користе се камиони корисне носивости 10 t Дневно радно време возила је 8 h Коефицијент искоришћења возног парка је 09 Роба се превози на палетама димензија a∙b∙c=08∙05∙038 m a тежина палете је 200 kg Димензије товарног сандука су А∙B∙C=60∙242∙26 m Утовар палета траје 50 minvoz a истовар 6 mint У повретку треба превести 3200 t робе чија је специфична запреминска тежина 03 tm3 Uтовар те робе је 40 minvoz а истовар 7mint време осталих задржавања је 1 h Саобраћајна брзина је 60 kmh Израчунати Ar Ai Uuk AK

Решење

Ако палете ређамо овако у једном Ако палете ређамо овако у једном

реду стаће n=7middot4=28 палета реду стаће n=12middot3=36 палета

Поставка

Усвојићемо начин ређања који омогућава да се превезе већи број палета n=36 палета

hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDZq

QukAr

o

o

o

ro

171min701107720min243720106

393171670720830

260

602239613932

12513968

72010

3620

17671660172010

7200

222

111

2211

1

11

1

11

==sdotsdot=sdotsdot===sdotsdot=sdotsdot=

=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDZq

QukAr

qgkCBA

ro

5335601110

3200

113110

306242206

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

==sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 19891890

17asymp===

α

tQukQukQuktkmKtQukUuk

10400320072006240006010400

21

1

=+=+==sdot=sdot=

kmZoKtArAK 20401602172 1 =sdotsdotsdot=sdotsdot=

A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

601

min7670min40

30

3200min6

830min506242206

202003805080

908

1060

72006072

2

2

32

1

1

1

1

===

===

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α

vozilaArAArAr r 17121 ==rArrgt

11 У периоду који има 120 дана потребно је организовати превоз 6200 t робе из места А у место Б удаљено 50 кm Транспорт се врши у равномерним дневним количинама а број радних дана је 96 Користе се камиони корисне носивости 20 t Дневно радно време возила је 9 h Коефицијент искоришћења возног парка је 095 Роба се превози на палетама димензија a∙b∙c=07∙04∙10 m a тежина палете је 300 kg Димензије товарног сандука су А∙B∙C=70∙242∙25 m Утовар палета траје 40 minvoz a истовар 5 mint У повретку треба превести 4200 t робе чија је специфична запреминска тежина 04 tm3 Uтовар те робе је 70 minvoz а истовар 8 mint време осталих задржавања је 40 min Саобраћајна брзина је 20 kmh Израчунати Ar Ai Uuk AK

Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoDrHrZ

qnGp

qQ

vozilaZq

QukAr

o

o

o

o

272min13685020851min9090205

61527217151670

520

502228116706155

776762811969

9020

6030

5474779020

6200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp=sdot

=sdot

=

=sdot

=sdot

==

asymp=sdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozZq

QukAr

qgkCBA

o

32137785020

4200

85020

405242207

2

22

2

asymp=sdotsdot

=sdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 62659505

asymp===α


10400420062005200005010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

20670min40

min8171min70

40

4200min5

670min405242207

30300014070

9509

2050

620096120

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

106122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α


14 У току месеца који има 30 дана (6 дана празника) треба организовати превоз 1872 t робе из места А у место C затим из места D у место А превести другу количину робе Коефицијент статичког искоришћења корисне носивости возила за прву врсту робе је 065 а за другу 088 Носивост возила је 24 t Радно време је 16 h а време осталих дангуба 450 минута Коефицијент искоришћења возног парка је 088 Време утовара прве робе је 10 mint a истовара 5 mint Време утовара друге врсте робе је 5 mint а истовара 120 minvoz Саобраћајне брзине које возила остварују VsA‐B=40 kmh VsB‐D=50 kmh VsC‐D=35 kmh VsB‐C=25 kmh Израчунати Ar Ai Quk Uuk

Поставка

C 105 km D

175km 135km

B

400km

A

Решење

vozArAi 17880

15===

α

tArZoqQuktQukQukQuk4253415888024

44406425341872

22

21


γ


hkmVshkmVshkmVshkmVsvoztitutitu

htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

25355040

min120min5

min5min10

88057min450

1624

8806501872

24

630

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZq

QukArAr

o

o

o

o

2min120761min6105880245

31min7865024562min1566502410

66727613162

73240400

50135

35105

25175

40400

864757667732

802886472416

15865024

1872

2

222

111

111

2211

1

11

====sdotsdot=sdotsdot=


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

=sdotsdot

=sdotsdot

==

γτγτγτ

γ

15 У току два месеца или 62 дана (има 10 дана празника) треба организовати превоз 2772 t робе из места А у место C затим из места D у место А превести другу количину робе Коефицијент статичког искоришћења корисне носивости возила за прву врсту робе је 085 а за другу 078 Носивост возила је 20 t Радно време је 16 h а време осталих дангуба 30 минута Коефицијент искоришћења возног парка је 078 Време утовара прве робе је 3 mint a истовара 10 mint Време утовара друге врсте робе је 8 mint а истовара 30 minvoz Саобраћајне брзине које возила остварују VsA‐B=30 kmh VsB‐D=45 kmh VsC‐D=50 kmh VsB‐C=35 kmh Израчунати Ar Ai Quk Uuk

Поставка C 65 km D

35km 45km

B

80km

A

Решење

vozArAi 48537803

asymp===α


6243352317802065205624332772

22

21


γ


hkmVshkmVshkmVshkmVs

voztitutitu

htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

35504530

min30min8min10min3

78050min30

1620

7808502772

52

1062

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrttoHrZ

vozilaDZq

QukArAr

o

o

o

ro

50min30082min8124780208

832min1708502010850min51850203

26650082832850

6483080

4545

5065

3535

3080

41550266648

1041415

16

314352185020

2772

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

γτγτγτ

γ

16 У току три месеца или 92 дана (12 дана празника) треба организовати превоз 4600 t робе из места А у место C затим из места D у место А превести 2570 t робе Коефицијент статичког искоришћења корисне носивости возила за прву врсту робе је 097 а за другу 082 Носивост возила је 22 t Радно време је 16 h а време осталих дангуба 240 минута Коефицијент искоришћења возног парка је 09 Време утовара прве робе је 10 mint a истовара 8 mint Време утовара друге врсте робе је 120 minvoz а истовара 9 mint Саобраћајне брзине које возила остварују VsA‐B=30 kmh VsB‐D=50 kmh VsC‐D=55 kmh VsB‐C=60 kmh Израчунати Ar Ai Quk Uuk

Поставка

C 80 km D

150km 95km

B

280km

A

Решење

vozArAi 87790

7asymp===

α

tQukQukQuk 71702570460021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

60555030

min92min120

min8min10

904min240

1622

820970

25704600

80

1292

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

712min36162820229852min72170970228

563min4213970221012117122852563

522430280

60150

5580

5095

30280

6439413115224

32293264398016

44543282022

2570

77463297022

4600

222

111

111

2211

2

22

1

11

==sdotsdot=sdotsdot===sdotsdot=sdotsdot===sdotsdot=sdotsdot=

=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γvozilaArAArAr r 7121 ==rArrgt

17 У току четири месеца или 120 дана (20 дана празника) треба организовати превоз 6500 t робе из места А у место C затим из места D у место А превести 8300 t робе Коефицијент статичког искоришћења корисне носивости возила за прву врсту робе је 087 а за другу 098 Носивост возила је 20 t Радно време је 16 h а време осталих дангуба 120 минута Коефицијент искоришћења возног парка је 088 Време утовара прве робе је 9 mint a истовара 12 mint Време утовара друге врсте робе је 120 minvoz а истовара 10 mint Саобраћајне брзине које возила остварују VsA‐B=60 kmh VsB‐D=30 kmh VsC‐D=50 kmh VsB‐C=30 kmh Израчунати Ar Ai Quk Uuk

Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ


18 У току месеца који има 30 дана (8 дана празника) треба организовати превоз 3932 t робе из места А у место C затим из места D у место А превести 5232 t робе Коефицијент статичког искоришћења корисне носивости возила за прву врсту робе је 077 а за другу 092 Носивост возила је 18 t Радно време је 16 h а време осталих дангуба 300 минута Коефицијент искоришћења возног парка је 098 Време утовара прве робе је 15 mint a истовара 9 mint Време утовара друге врсте робе је 180 minvoz а истовара 7 mint Саобраћајне брзине које возила остварују VsA‐B=40 kmh VsB‐D=30 kmh VsC‐D=45 kmh VsB‐C=20 kmh Израчунати Ar Ai Quk Uuk

Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ


19 У току трећег квартала у коме се ради 65 дана потребно је организовати превоз 8320000 литара нафте тегљачима са полуприколицама носивости 5 t на растојање од 2271 km Нафта се пуни у бурад чији је пречник 58 cm а висина 7574 cm Димензије товарног простора су АxBxC=50x24x10m Бурад се у товарни простор слажу усправно Време утовара бурета једнако је времену истовара и износе 2 minbur а време откачињања и прикачињања полуприколиве је 5 min Радно време возног парка је 16 h Саобраћајна брзина је 58 kmh Израчунат потребан број полуприколица


У товарни сандук стаје n= 8x4=32 бурета

Запремина једног бурета

huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1

1 VstopKttoptuiVsAtP icepoluprikol138812

)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot

20 У току четири месеца у коме се ради 100 дана потребно је организовати превоз 7350000 литара нафте возилима носивости 8 t на растојање од 1782 km Нафта се пуни у бурад чији је пречник 80 cm а висина 6967 cm Димензије товарног простора су АxBxC=60x24x10m Бурад се у товарни простор слажу усправно Време утовара бурета једнако је времену истовара и износе 5 minbur а време откачињања и прикачињања полуприколиве је 10 min Радно време возног парка је 16 h Саобраћајна брзина је 40 kmh Израчунати потребан број полуприколица

Решење

У товарни сандук стаје n= 7x3=21 буре

hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===

ττ( ) lmHrVbur 2002075740143290 322 ==sdotsdot== π

Поставка Запремина једног бурета

Укупан број потребних вожњи

vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ

Број вожњи у току дана

huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot

21 У току 55 дана потребно је организовати превоз 5550000 литара нафте тегљачима са полуприколицама носивости 10 t на растојање од 150 km Нафта се пуни у бурад чији је пречник 80 cm а висина 80 cm Димензије товарног простора су АxBxC=80x24x10m Бурад се у товарни простор слажу усправно Време утовара бурета једнако је времену истовара и износе 4 minbur а време откачињања и прикачињања полуприколиве је 8 min Радно време возног парка је 16 h Саобраћајна брзина је 45 kmh Израчунати потребан број полуприколица




hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ

( ) lmHrVbur 35035006967014340 322 ==sdotsdot== π

=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdotsdot+sdot

+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==


24 На линији ЈГПП‐а потребно је израчунати за вршни и ванвршни период број потребних возила на раду број путника по часу број полазака по часу интервал возила Познати су следећи подаци дужина линије у једном смеру 10 кm саобраћајна брзина 20 kmh линија има 9 стајалишта у једном смеру и два терминуса време задржавања на стајалишту износи 10 s а на терминусу 5 min Број путника који треба да се превезу у току дана 15120 возила су капацитета 90 места коефицијент попуњености за ванвршно оптерећење износи 08 а за вршно 1 степен измене путника износи 18 за ванвршно и 3 за вршно оптерећење Коефицијент неравномерности је 19 Радно време је 8 h а време вршног оптерећења 3 h(13‐16h) Урадити и график реда вожње за један полазак у вршном времену оптерећења

Поставка

Решење

Време потребно да возило пређе од почетне до крајње станице

min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==

=++sdotsdot+=++sdot+=

hVsKltw

tktptsitwto

o

o

У једном смеру 32 а у другом 31 минут

km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==

asymp=++sdotsdot+=++sdot+=

hVsKltw

tktptsitwto

o

o


У једном смеру 38 а у другом 39 минута

km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h

27 На линији ЈГПП‐а потребно је израчунати за вршни и ванвршни период број потребних возила на раду број путника по часу број полазака по часу интервал возила Познати су следећи подаци дужина линије у једном смеру 12 кm саобраћајна брзина 30 kmh линија има 9 стајалишта у једном смеру и два терминуса време задржавања на стајалишту износи 20 s а на терминусу 15 min Број путника који треба да се превезу у току дана 29200 возила су капацитета 90 места коефицијент попуњености за ванвршно оптерећење износи 08 а за вршно 1 степен измене путника износи 22 за ванвршно и 23 за вршно оптерећење Коефицијент неравномерности је 12 Радно време је 8h а време вршног оптерећења 3 h(14‐17h) Урадити и график реда вожње за један полазак у ванвршном времену оптерећењаако прво возило полази у 5h

Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482

asymp=sdot+=sdot+ tsitwo

28 На линији ЈГПП‐а потребно је израчунати за вршни и ванвршни период број потребних возила на раду број путника по часу број полазака по часу интервал возила Познати су следећи подаци дужина линије у једном смеру 20 кm саобраћајна брзина 20 kmh линија има 7 стајалишта у једном смеру и два терминуса време задржавања на стајалишту износи 10 s а на терминусу 10 min Број путника који треба да се превезу у току дана 32000 возила су капацитета 100 места коефицијент попуњености за ванвршно оптерећење износи 07 а за вршно 1 степен измене путника износи 25 и за ванвршно и за вршно оптерећење Коефицијент неравномерности је 21 Радно време је 20 h а време вршног оптерећења 4 h(13‐17h) Урадити и график реда вожње за један полазак у вршном времену оптерећења

Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h

29 а)Возила раде по прстенастом путу вожње као на слици Растојања између тачака су LAB=30 km LBC=24 km LCD=15 km LDA=42 km Количине робе које треба транспортовати су QAB=10 t QBC=8 t QDA=9 t Просечна саобраћајна брзина је Vs= 30kmh а време утоварно истоварне манипулације је tu=ti=20min Време рада возила у току дана је Hr=12h

bull Колико циклуса возило може да оствари у току дана

bull Колики је обим транспорта и транспортног рада

bull Колико је искоришћење тређеног пута β

bull Колика је експлоатациона брзина возила

LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL

tt +++++++++=60middot60middot60middot60middot

2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=

bull Број обрта у току дана је

obrtatHZoO

R 21275

12asymp===

bull Обим транспорта (количина превезеног терета)

tQQQQdn DABCAB 279810 =++=++=

Транспортни рад

kmtQLQLQLUdn DADABCBCABAB middot87042middot98middot2430middot10middotmiddotmiddot =++=++=

bull Коефицијент пређеног пута

86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ

bull Експлоатациона брзина

hkmtKVo

e 471975

111===

б) За прстенасти пут вожње познати су следећи подаци носивост возила q = 4 t Kt1 = 16 km Kp1 1=4 km Kt2 = 6 km Kt3 = 8 km Kp2 = 4 km γ1 = 1 γ2 = 08 γ3=09 Време утовара и истовара tui1=24 min tui2=30 min tui3=48 min Радно време је 15 h нулти пређени пут је Kn1+Kn2=10 km а саобраћајна брзина је Vs = 20 kmh Израчунати γsr Kstλ βo Q1dn U1dn

Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs

KpKpKtKtKt 21321 ++++

two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=

tZosrqndnQ 2439048490431 =sdot=sdotsdotsdot=sdotsdotsdot= γ

tkmiKtiqZodnUn

448)908806116(44)(1

1 =sdot+sdot+sdotsdotsdot=sdotsdot= sum γ

в) За збирни пут вожње познати су следећи подаци

Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t

Возило без терета прeђе Kp = 2 km Носивост возила је q = 35 t саобраћајна брзина је Vs = 20 kmh време утовара и истовара у току обрта је tui = 12 h Израчунати γsr to и остварени транспортни рад у току једног обрта

РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h

U 443213321221111 Kt)QQQQ(Kt)QQQ(Kt)QQ(KtQ +++++++++sdot=

U 94871310916114401 =sdot+sdot+sdot+sdot= tkm






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=

60middot60middot60middot60middot

3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===

б) За прстенасти пут вожње познати су следећи подаци носивост возила q = 8 t Kt1 = 18 km Kp1=6 km Kt2 = 9 km Kt3 = 8 km Kp2 = 8 km γ1 = 1 γ2 = 07 γ3=09 Време утовара и истовара tui1=20 min tui2=35 min tui3=40 min Радно време је 16 h нулти пређени пут је Kn1+Kn2=11 km а саобраћајна брзина је Vs = 30 kmh Израчунати γsr Kstλ βo Q1dn U1dn

Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum

hntuitwto o 2235303631 =sdot+=sdot+=

hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=

tZosrqndnQ 41045870831 =sdotsdotsdot=sdotsdotsdot= γ

tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h

443213321221111 )()()( KtQQQQKtQQQKtQQKtQU +++++++++sdot=

tkmU 83966212418709201 =sdot+sdot+sdot+sdot=






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===

б) За прстенасти пут вожње познати су следећи подаци носивост возила q = 10 t Kt1 = 20 km Kp1=8 km Kt2 = 12 km Kt3 =15 km Kp2 =8 km γ1 = 09 γ2 = 06 γ3=08 Време утовара и истовара tui1=10 min tui2=15 min tui3=20 min Радно време је 12 h нулти пређени пут је Kn1+Kn2=4 km а саобраћајна брзина је Vs = 20 kmh Израчунати γsr Kstλ βo Q1dn U1dn

Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t

Возило без терета прeђе Kp = 9 km Носивост возила је q = 9 t саобраћајна брзина је Vs = 30 kmh време утовара и истовара у току обрта је tui = 30 мин Израчунати γsr to и остварени транспортни рад у току једног обрта

РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=



33 Дати ду следећи подаци

bull Потрошња горива Pgor=14 l100km

bull Цена горива Cgor=110 dinl

bull Количина уља у кориту за уље мотора Vmu=9 l

bull Периодичност замене уља Kmu=3 000 km

bull Цена моторног уља Cmu=540 dinl

bull Број гума на возилуNg=6

bull Цена једне гуме Cg=20 000 din

bull Век трајања гуме Kg=40 000km

bull Цена возила Cv=10 500 000din

bull Годишња километражаKgod=50 000 km

bull Век трајања возила Kv=250 000 km

bull Годишњи трошкови регистрације возила Cr=55 000 din

Израчунати погонске трошкове и трошкове годишње амортизације за пређени пут возила од К=9 500km и остварени транспортни рад од U=19 000 km

Погонски трошкови

‐Трошкови горива

‐Трошкови моторног уља

‐Трошкови гума

Укупни трошкови погонског материјала

Укупни погонски трошкови за пређени пут од К=9500 km

‐Трошкови амортизације

‐Трошкови осигурања и регистрације

kmdinCgorPgorTgor 415100

11014100

=sdot

=sdot

=

tkmdinUKCgorPgorTgor 77

190009500

10011014

100=sdot

sdot=sdot

sdot=

kmdinCmuPmuTmu 621100

54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=

tkmdinUKCmuPmuTmu 810

190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=

kmdinTgTmuTgorTpm 02203621415 =++=++=

tkmdinTgTmuTgorTpm 01105181077 =++=++=

dinKTpmTpmuk 19019095000220 =sdot=sdot=

kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===

Укупни трошкови по једном километру

Укупни трошкови по тона‐ километру

Укупни трошкови за пређени пут од 9500 km

б) Израчунати број места за утовар и места за истовар као и интервал вожње под условом да возила не чекају и да станица ради без застоја ако су дати следећи подаци Ar=30 vozila Kt1=10 km β=05 γ=08 q=5 t Vs = 20 kmh tu=8 minvoz ti=12 minvoz

РЕШЕЊЕ

to = two + tui Vs=twoKo

two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h

to = two + tui = 1 + 033 = 133 h ili to = 80 min

Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr

45 mesta asymp 4 места

Интервал вожње ће бити

Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=

kmdinTorTamTpmT 126311420220 =++=++=

tkmdinTorTamTpmT 5631550210110 =++=++=

dinKTTuk 59964095001263 =sdot=sdot=











bull Годишња километража Kgod=60 000 km










10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=




38 Из складишта S потребно је у току једног дана транспортовати цемент и то 2700 t до три градилишта A B и C На свако градилиште треба однети исту количину цемента Статички коефицијент искоришћења носивости возила је 1 радно време 12 h коефицијент техничке исправности возног парка 1 а коефицијент искоришћења исправног возног парка такође 1 Носивост возила је 15 t Остали подаци дати су у табели

A

B

G S

C

За радијални пут вожње израчунати

Број возила на раду и инвентарски број возила

Укупно извршени транспортни рад

Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

релације Kt (km) Vs (kmh)

tu ti tos

S‐A 15 20 2 mint 10 min 10 min

S‐B 30 30 2 mint 10 min 5 min

S‐C 35 35 2 mint 20 min 10 min

S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

tkmKtQdnKtQdnKtQdnUdnt

vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321

=++sdot=sdot+sdot+sdot==sdot=primesdot=

===

=++=++=

αααα

39 Из складишта S потребно је у току једног дана транспортовати цемент и то 2400 t до три градилишта A B и C На свако градилиште треба однети исту количину цемента Статички коефицијент искоришћења носивости возила је 09 радно време 16 h коефицијент техничке исправности возног парка 1 а коефицијент искоришћења исправног возног парка 09 Носивост возила је 12 t Остали подаци дати су у табели

A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


C G

30km 6 km

B 70km A


htoshkmVs

voztitumotui

tqhH

tkgGtQukmotoraMuk

danaDdanaD

r

m

r

i

1080

90min25

min105

1580800

760018000

180195

2

22

1

2

===

===

==

====

==

γ

τ


hVsKttw

htostuitwto

obrtatoVsK

HrZ

tGMukQuk

vozilaDZq

QukA

o

o

n

o

m

ror

830min5025251min60610

3318301

528010022

4341083152

335343480

62152

144008018000

5180315

14400

222

11

21

1

1

1

11

==+=+===sdot=sdot=

=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=minus

=

=sdot=sdot=

=sdotsdotsdot

=sdotsdotsdot

=

τ

γ

vozDZq

QukA

motGqn

ror

m

31331803905

7600

62568051

2

22

1

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdot

=sdot

=

γ

γ





C G

50km 4km

B 90km A


htoshkmVs

voztitumotui

tqhH

tkgGtQukmotoraMuk

danaDdanaD

r

m

r

i

15060

80min15

min206

1270700

450020000

150200

2

22

1

2

===

===

==

====

==

γ

τ

htitutuihnuitui

htuituitui

hVsKttw

htostuitwto

obrtatoVsK

HrZ

tGMukQuk

vozilaDZq

QukA

o

o

n

o

m

ror

50min30151562min160820

135062

646014022

8571501364

2891857

604215

2

140007020000

8787150216

14000

222

11

21

1

1

1

11

==+=+===sdot=sdot=

=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=minus

=

=sdot=sdot=

asymp=sdotsdotsdot

=sdotsdotsdot

=

τ

γ

vozDZq

QukA

motGqn

ror

m

31331502806

4500

85787061

2

22

1

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdot

=sdot

=

γ

γ





C G

30km 7km

B 55km A


htoshkmVs

voztitumotui

tqhH

tkgGtQukmotoraMuk

danaDdanaD

r

m

r

i

450

930min14

min404

1290900

560014000

200220

2

22

1

2

===

===

==

====

==

γ

τ

htitutuihnuitui

htuituitui

hVsKttw

htostuitwto

obrttoVsK

HrZ

tGMukQuk

vozilaDZq

QukA

o

o

n

o

m

ror

470min281414672min160440

34062

4350

85224104343

1111541050

72122

126009014000

16200114

12600

222

11

21

1

1

1

11

==+=+===sdot=sdot=

=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=minus

=

=sdot=sdot=

=sdotsdotsdot

=sdotsdotsdot

=

τ

γ

vozDZq

QukA

motGqn

ror

m

853720029304

5600

44449041

2

22

1

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdot

=sdot

=

γ

γ





C G

45km 8km

B 90km A


htoshkmVs

voztitumotui

tqhH

tkgGtQukmotoraMuk

danaDdanaD

r

m

r

i

145

950min42

min133

1690900

965016000

150200

2

22

1

2

===

===

==

====

==

γ

τ


hVsKttw

htostuitwto

obrtatoVsK

HrZ

tGMukQuk

vozilaDZq

QukA

o

o

n

o

m

ror

41min844242650min39313

05241650

64513522

05910526

2059

458216

2

144009016000

16150213

14400

222

11

21

1

1

1

11

==+=+===sdot=sdot=

=+=+=

=sdot

==

=++=++=

=

sdotminus

=minus

=

=sdot=sdot=

=sdotsdotsdot

=sdotsdotsdot

=

τ

γ

vozDZq

QukA

motGqn

ror

m

11281115029503

9650

3339031

2

22

1

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdot

=sdot

=

γ

γ





Решење


Di=60dana

1802

7016

30min2

650214257

21420526

8046800

46

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituituituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

780min846902627822780

33530

8022118782335

2971118

16

141144629026

304203042065046800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 9026

650214257650214205=


vozilaArAi 1851780

14asymp===



tkmKtQukUuk

363248346142970263662903363248330420

85032268807264966

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 97026

7021425770214205=


660118335

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

38488161446

85032268

161614463662903

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

15194601824

8503226824

4326018243662903

24

=sdotsdot

==

=sdotsdot

==

6702416

24===

Hrρ


Решење


Di=50dana

1603

9014

40min3

750512256

51220536

6036800

36

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

421min32857903634243421

340

60224274243

2881427

14

13471336279036

276002760075036800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 79036

750512256750512205=


vozilaArAi 22662160

13asymp===



tkmKtQukUuk

243167436132940362459274243167427600

43556454602459274

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 94026

9051225690512205=


404273

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

80542141336

43556454

0491413362459274

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

71134502224

4355645424

2525022242459274

24

=sdotsdot

==

=sdotsdot

==

5802414

24===

Hrρ


Решење


Di=90dana

1903

8016

40min8

440512207

51220532

4016800

72

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

32min2413854032835332

240

402237352

219237

16

397272254032

7392739244016800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 54032

440512207440512205=


vozilaArAi 333390

3asymp===



tkmKtQukUuk

7613685723299032762107776136857392

4843110407621077

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 99032

8051220780512205=


27037

2===

totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

9624316372

4843110

16163727621077

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

6416272324

484311024

074723247621077

24

=sdotsdot

==

=sdotsdot

==

6702416

24===

Hrρ


Решење


Di=30dana

90904

4012

30min12

5505142257

514220833

40023800

24

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoDrHrZ

vozilaZq

QukAA

tgkVQuk

o

orr

26min243729403312210426

67263040022

87362106726

881787362412

537552894033

130901309055023800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 94033

55051422575505142208=



53asymp===


tArZoqQuktQukQukQuk

tkmKtQukUuk

56951453868033562260456951413090

523600040013090

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 68033

405142257405142208=


72087366726

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

03343125324

5236000

4811253245622604

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

73154306624

523600024

6703066245622604

24

=sdotsdot

==

=sdotsdot

==

502412

24===

Hrρ


Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDZq

QukAr

o

o

o

ro

171min701107720min243720106

393171670720830

260

602239613932

12513968

72010

3620

17671660172010

7200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDZq

QukAr

qgkCBA

ro

5335601110

3200

113110

306242206

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

==sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 19891890

17asymp===

α


10400320072006240006010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

601

min7670min40

30

3200min6

830min506242206

202003805080

908

1060

72006072

2

2

32

1

1

1

1

===

===

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoDrHrZ

qnGp

qQ

vozilaZq

QukAr

o

o

o

o

272min13685020851min9090205

61527217151670

520

502228116706155

776762811969

9020

6030

5474779020

6200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp=sdot

=sdot

=

=sdot

=sdot

==

asymp=sdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozZq

QukAr

qgkCBA

o

32137785020

4200

85020

405242207

2

22

2

asymp=sdotsdot

=sdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 62659505

asymp===α


10400420062005200005010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

20670min40

min8171min70

40

4200min5

670min405242207

30300014070

9509

2050

620096120

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

106122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Поставка

C 105 km D

175km 135km

B

400km

A

Решење

vozArAi 17880

15===

α


44406425341872

22

21


γ



htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

25355040

min120min5

min5min10

88057min450

1624

8806501872

24

630

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZq

QukArAr

o

o

o

o

2min120761min6105880245

31min7865024562min1566502410

66727613162

73240400

50135

35105

25175

40400

864757667732

802886472416

15865024

1872

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

=sdotsdot

=sdotsdot

==

γτγτγτ

γ



35km 45km

B

80km

A

Решење

vozArAi 48537803

asymp===α


6243352317802065205624332772

22

21


γ



voztitutitu

htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

35504530

min30min8min10min3

78050min30

1620

7808502772

52

1062

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrttoHrZ

vozilaDZq

QukArAr

o

o

o

ro

50min30082min8124780208

832min1708502010850min51850203

26650082832850

6483080

4545

5065

3535

3080

41550266648

1041415

16

314352185020

2772

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

γτγτγτ

γ


Поставка

C 80 km D

150km 95km

B

280km

A

Решење

vozArAi 87790

7asymp===

α

tQukQukQuk 71702570460021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

60555030

min92min120

min8min10

904min240

1622

820970

25704600

80

1292

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

712min36162820229852min72170970228

563min4213970221012117122852563

522430280

60150

5580

5095

30280

6439413115224

32293264398016

44543282022

2570

77463297022

4600

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ



Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ



Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


C G

50km 4km

B 90km A


htoshkmVs

voztitumotui

tqhH

tkgGtQukmotoraMuk

danaDdanaD

r

m

r

i

15060

80min15

min206

1270700

450020000

150200

2

22

1

2

===

===

==

====

==

γ

τ

htitutuihnuitui

htuituitui

hVsKttw

htostuitwto

obrtatoVsK

HrZ

tGMukQuk

vozilaDZq

QukA

o

o

n

o

m

ror

50min30151562min160820

135062

646014022

8571501364

2891857

604215

2

140007020000

8787150216

14000

222

11

21

1

1

1

11

==+=+===sdot=sdot=

=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=minus

=

=sdot=sdot=

asymp=sdotsdotsdot

=sdotsdotsdot

=

τ

γ

vozDZq

QukA

motGqn

ror

m

31331502806

4500

85787061

2

22

1

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdot

=sdot

=

γ

γ





C G

30km 7km

B 55km A


htoshkmVs

voztitumotui

tqhH

tkgGtQukmotoraMuk

danaDdanaD

r

m

r

i

450

930min14

min404

1290900

560014000

200220

2

22

1

2

===

===

==

====

==

γ

τ

htitutuihnuitui

htuituitui

hVsKttw

htostuitwto

obrttoVsK

HrZ

tGMukQuk

vozilaDZq

QukA

o

o

n

o

m

ror

470min281414672min160440

34062

4350

85224104343

1111541050

72122

126009014000

16200114

12600

222

11

21

1

1

1

11

==+=+===sdot=sdot=

=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=minus

=

=sdot=sdot=

=sdotsdotsdot

=sdotsdotsdot

=

τ

γ

vozDZq

QukA

motGqn

ror

m

853720029304

5600

44449041

2

22

1

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdot

=sdot

=

γ

γ





C G

45km 8km

B 90km A


htoshkmVs

voztitumotui

tqhH

tkgGtQukmotoraMuk

danaDdanaD

r

m

r

i

145

950min42

min133

1690900

965016000

150200

2

22

1

2

===

===

==

====

==

γ

τ


hVsKttw

htostuitwto

obrtatoVsK

HrZ

tGMukQuk

vozilaDZq

QukA

o

o

n

o

m

ror

41min844242650min39313

05241650

64513522

05910526

2059

458216

2

144009016000

16150213

14400

222

11

21

1

1

1

11

==+=+===sdot=sdot=

=+=+=

=sdot

==

=++=++=

=

sdotminus

=minus

=

=sdot=sdot=

=sdotsdotsdot

=sdotsdotsdot

=

τ

γ

vozDZq

QukA

motGqn

ror

m

11281115029503

9650

3339031

2

22

1

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdot

=sdot

=

γ

γ





Решење


Di=60dana

1802

7016

30min2

650214257

21420526

8046800

46

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituituituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

780min846902627822780

33530

8022118782335

2971118

16

141144629026

304203042065046800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 9026

650214257650214205=


vozilaArAi 1851780

14asymp===



tkmKtQukUuk

363248346142970263662903363248330420

85032268807264966

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 97026

7021425770214205=


660118335

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

38488161446

85032268

161614463662903

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

15194601824

8503226824

4326018243662903

24

=sdotsdot

==

=sdotsdot

==

6702416

24===

Hrρ


Решење


Di=50dana

1603

9014

40min3

750512256

51220536

6036800

36

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

421min32857903634243421

340

60224274243

2881427

14

13471336279036

276002760075036800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 79036

750512256750512205=


vozilaArAi 22662160

13asymp===



tkmKtQukUuk

243167436132940362459274243167427600

43556454602459274

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 94026

9051225690512205=


404273

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

80542141336

43556454

0491413362459274

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

71134502224

4355645424

2525022242459274

24

=sdotsdot

==

=sdotsdot

==

5802414

24===

Hrρ


Решење


Di=90dana

1903

8016

40min8

440512207

51220532

4016800

72

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

32min2413854032835332

240

402237352

219237

16

397272254032

7392739244016800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 54032

440512207440512205=


vozilaArAi 333390

3asymp===



tkmKtQukUuk

7613685723299032762107776136857392

4843110407621077

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 99032

8051220780512205=


27037

2===

totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

9624316372

4843110

16163727621077

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

6416272324

484311024

074723247621077

24

=sdotsdot

==

=sdotsdot

==

6702416

24===

Hrρ


Решење


Di=30dana

90904

4012

30min12

5505142257

514220833

40023800

24

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoDrHrZ

vozilaZq

QukAA

tgkVQuk

o

orr

26min243729403312210426

67263040022

87362106726

881787362412

537552894033

130901309055023800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 94033

55051422575505142208=



53asymp===


tArZoqQuktQukQukQuk

tkmKtQukUuk

56951453868033562260456951413090

523600040013090

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 68033

405142257405142208=


72087366726

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

03343125324

5236000

4811253245622604

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

73154306624

523600024

6703066245622604

24

=sdotsdot

==

=sdotsdot

==

502412

24===

Hrρ


Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDZq

QukAr

o

o

o

ro

171min701107720min243720106

393171670720830

260

602239613932

12513968

72010

3620

17671660172010

7200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDZq

QukAr

qgkCBA

ro

5335601110

3200

113110

306242206

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

==sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 19891890

17asymp===

α


10400320072006240006010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

601

min7670min40

30

3200min6

830min506242206

202003805080

908

1060

72006072

2

2

32

1

1

1

1

===

===

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoDrHrZ

qnGp

qQ

vozilaZq

QukAr

o

o

o

o

272min13685020851min9090205

61527217151670

520

502228116706155

776762811969

9020

6030

5474779020

6200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp=sdot

=sdot

=

=sdot

=sdot

==

asymp=sdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozZq

QukAr

qgkCBA

o

32137785020

4200

85020

405242207

2

22

2

asymp=sdotsdot

=sdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 62659505

asymp===α


10400420062005200005010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

20670min40

min8171min70

40

4200min5

670min405242207

30300014070

9509

2050

620096120

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

106122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Поставка

C 105 km D

175km 135km

B

400km

A

Решење

vozArAi 17880

15===

α


44406425341872

22

21


γ



htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

25355040

min120min5

min5min10

88057min450

1624

8806501872

24

630

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZq

QukArAr

o

o

o

o

2min120761min6105880245

31min7865024562min1566502410

66727613162

73240400

50135

35105

25175

40400

864757667732

802886472416

15865024

1872

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

=sdotsdot

=sdotsdot

==

γτγτγτ

γ



35km 45km

B

80km

A

Решење

vozArAi 48537803

asymp===α


6243352317802065205624332772

22

21


γ



voztitutitu

htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

35504530

min30min8min10min3

78050min30

1620

7808502772

52

1062

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrttoHrZ

vozilaDZq

QukArAr

o

o

o

ro

50min30082min8124780208

832min1708502010850min51850203

26650082832850

6483080

4545

5065

3535

3080

41550266648

1041415

16

314352185020

2772

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

γτγτγτ

γ


Поставка

C 80 km D

150km 95km

B

280km

A

Решење

vozArAi 87790

7asymp===

α

tQukQukQuk 71702570460021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

60555030

min92min120

min8min10

904min240

1622

820970

25704600

80

1292

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

712min36162820229852min72170970228

563min4213970221012117122852563

522430280

60150

5580

5095

30280

6439413115224

32293264398016

44543282022

2570

77463297022

4600

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ



Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ



Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


C G

30km 7km

B 55km A


htoshkmVs

voztitumotui

tqhH

tkgGtQukmotoraMuk

danaDdanaD

r

m

r

i

450

930min14

min404

1290900

560014000

200220

2

22

1

2

===

===

==

====

==

γ

τ

htitutuihnuitui

htuituitui

hVsKttw

htostuitwto

obrttoVsK

HrZ

tGMukQuk

vozilaDZq

QukA

o

o

n

o

m

ror

470min281414672min160440

34062

4350

85224104343

1111541050

72122

126009014000

16200114

12600

222

11

21

1

1

1

11

==+=+===sdot=sdot=

=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=minus

=

=sdot=sdot=

=sdotsdotsdot

=sdotsdotsdot

=

τ

γ

vozDZq

QukA

motGqn

ror

m

853720029304

5600

44449041

2

22

1

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdot

=sdot

=

γ

γ





C G

45km 8km

B 90km A


htoshkmVs

voztitumotui

tqhH

tkgGtQukmotoraMuk

danaDdanaD

r

m

r

i

145

950min42

min133

1690900

965016000

150200

2

22

1

2

===

===

==

====

==

γ

τ


hVsKttw

htostuitwto

obrtatoVsK

HrZ

tGMukQuk

vozilaDZq

QukA

o

o

n

o

m

ror

41min844242650min39313

05241650

64513522

05910526

2059

458216

2

144009016000

16150213

14400

222

11

21

1

1

1

11

==+=+===sdot=sdot=

=+=+=

=sdot

==

=++=++=

=

sdotminus

=minus

=

=sdot=sdot=

=sdotsdotsdot

=sdotsdotsdot

=

τ

γ

vozDZq

QukA

motGqn

ror

m

11281115029503

9650

3339031

2

22

1

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdot

=sdot

=

γ

γ





Решење


Di=60dana

1802

7016

30min2

650214257

21420526

8046800

46

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituituituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

780min846902627822780

33530

8022118782335

2971118

16

141144629026

304203042065046800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 9026

650214257650214205=


vozilaArAi 1851780

14asymp===



tkmKtQukUuk

363248346142970263662903363248330420

85032268807264966

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 97026

7021425770214205=


660118335

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

38488161446

85032268

161614463662903

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

15194601824

8503226824

4326018243662903

24

=sdotsdot

==

=sdotsdot

==

6702416

24===

Hrρ


Решење


Di=50dana

1603

9014

40min3

750512256

51220536

6036800

36

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

421min32857903634243421

340

60224274243

2881427

14

13471336279036

276002760075036800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 79036

750512256750512205=


vozilaArAi 22662160

13asymp===



tkmKtQukUuk

243167436132940362459274243167427600

43556454602459274

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 94026

9051225690512205=


404273

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

80542141336

43556454

0491413362459274

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

71134502224

4355645424

2525022242459274

24

=sdotsdot

==

=sdotsdot

==

5802414

24===

Hrρ


Решење


Di=90dana

1903

8016

40min8

440512207

51220532

4016800

72

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

32min2413854032835332

240

402237352

219237

16

397272254032

7392739244016800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 54032

440512207440512205=


vozilaArAi 333390

3asymp===



tkmKtQukUuk

7613685723299032762107776136857392

4843110407621077

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 99032

8051220780512205=


27037

2===

totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

9624316372

4843110

16163727621077

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

6416272324

484311024

074723247621077

24

=sdotsdot

==

=sdotsdot

==

6702416

24===

Hrρ


Решење


Di=30dana

90904

4012

30min12

5505142257

514220833

40023800

24

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoDrHrZ

vozilaZq

QukAA

tgkVQuk

o

orr

26min243729403312210426

67263040022

87362106726

881787362412

537552894033

130901309055023800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 94033

55051422575505142208=



53asymp===


tArZoqQuktQukQukQuk

tkmKtQukUuk

56951453868033562260456951413090

523600040013090

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 68033

405142257405142208=


72087366726

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

03343125324

5236000

4811253245622604

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

73154306624

523600024

6703066245622604

24

=sdotsdot

==

=sdotsdot

==

502412

24===

Hrρ


Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDZq

QukAr

o

o

o

ro

171min701107720min243720106

393171670720830

260

602239613932

12513968

72010

3620

17671660172010

7200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDZq

QukAr

qgkCBA

ro

5335601110

3200

113110

306242206

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

==sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 19891890

17asymp===

α


10400320072006240006010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

601

min7670min40

30

3200min6

830min506242206

202003805080

908

1060

72006072

2

2

32

1

1

1

1

===

===

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoDrHrZ

qnGp

qQ

vozilaZq

QukAr

o

o

o

o

272min13685020851min9090205

61527217151670

520

502228116706155

776762811969

9020

6030

5474779020

6200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp=sdot

=sdot

=

=sdot

=sdot

==

asymp=sdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozZq

QukAr

qgkCBA

o

32137785020

4200

85020

405242207

2

22

2

asymp=sdotsdot

=sdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 62659505

asymp===α


10400420062005200005010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

20670min40

min8171min70

40

4200min5

670min405242207

30300014070

9509

2050

620096120

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

106122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Поставка

C 105 km D

175km 135km

B

400km

A

Решење

vozArAi 17880

15===

α


44406425341872

22

21


γ



htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

25355040

min120min5

min5min10

88057min450

1624

8806501872

24

630

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZq

QukArAr

o

o

o

o

2min120761min6105880245

31min7865024562min1566502410

66727613162

73240400

50135

35105

25175

40400

864757667732

802886472416

15865024

1872

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

=sdotsdot

=sdotsdot

==

γτγτγτ

γ



35km 45km

B

80km

A

Решење

vozArAi 48537803

asymp===α


6243352317802065205624332772

22

21


γ



voztitutitu

htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

35504530

min30min8min10min3

78050min30

1620

7808502772

52

1062

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrttoHrZ

vozilaDZq

QukArAr

o

o

o

ro

50min30082min8124780208

832min1708502010850min51850203

26650082832850

6483080

4545

5065

3535

3080

41550266648

1041415

16

314352185020

2772

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

γτγτγτ

γ


Поставка

C 80 km D

150km 95km

B

280km

A

Решење

vozArAi 87790

7asymp===

α

tQukQukQuk 71702570460021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

60555030

min92min120

min8min10

904min240

1622

820970

25704600

80

1292

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

712min36162820229852min72170970228

563min4213970221012117122852563

522430280

60150

5580

5095

30280

6439413115224

32293264398016

44543282022

2570

77463297022

4600

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ



Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ



Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


C G

45km 8km

B 90km A


htoshkmVs

voztitumotui

tqhH

tkgGtQukmotoraMuk

danaDdanaD

r

m

r

i

145

950min42

min133

1690900

965016000

150200

2

22

1

2

===

===

==

====

==

γ

τ


hVsKttw

htostuitwto

obrtatoVsK

HrZ

tGMukQuk

vozilaDZq

QukA

o

o

n

o

m

ror

41min844242650min39313

05241650

64513522

05910526

2059

458216

2

144009016000

16150213

14400

222

11

21

1

1

1

11

==+=+===sdot=sdot=

=+=+=

=sdot

==

=++=++=

=

sdotminus

=minus

=

=sdot=sdot=

=sdotsdotsdot

=sdotsdotsdot

=

τ

γ

vozDZq

QukA

motGqn

ror

m

11281115029503

9650

3339031

2

22

1

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdot

=sdot

=

γ

γ





Решење


Di=60dana

1802

7016

30min2

650214257

21420526

8046800

46

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituituituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

780min846902627822780

33530

8022118782335

2971118

16

141144629026

304203042065046800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 9026

650214257650214205=


vozilaArAi 1851780

14asymp===



tkmKtQukUuk

363248346142970263662903363248330420

85032268807264966

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 97026

7021425770214205=


660118335

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

38488161446

85032268

161614463662903

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

15194601824

8503226824

4326018243662903

24

=sdotsdot

==

=sdotsdot

==

6702416

24===

Hrρ


Решење


Di=50dana

1603

9014

40min3

750512256

51220536

6036800

36

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

421min32857903634243421

340

60224274243

2881427

14

13471336279036

276002760075036800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 79036

750512256750512205=


vozilaArAi 22662160

13asymp===



tkmKtQukUuk

243167436132940362459274243167427600

43556454602459274

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 94026

9051225690512205=


404273

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

80542141336

43556454

0491413362459274

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

71134502224

4355645424

2525022242459274

24

=sdotsdot

==

=sdotsdot

==

5802414

24===

Hrρ


Решење


Di=90dana

1903

8016

40min8

440512207

51220532

4016800

72

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

32min2413854032835332

240

402237352

219237

16

397272254032

7392739244016800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 54032

440512207440512205=


vozilaArAi 333390

3asymp===



tkmKtQukUuk

7613685723299032762107776136857392

4843110407621077

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 99032

8051220780512205=


27037

2===

totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

9624316372

4843110

16163727621077

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

6416272324

484311024

074723247621077

24

=sdotsdot

==

=sdotsdot

==

6702416

24===

Hrρ


Решење


Di=30dana

90904

4012

30min12

5505142257

514220833

40023800

24

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoDrHrZ

vozilaZq

QukAA

tgkVQuk

o

orr

26min243729403312210426

67263040022

87362106726

881787362412

537552894033

130901309055023800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 94033

55051422575505142208=



53asymp===


tArZoqQuktQukQukQuk

tkmKtQukUuk

56951453868033562260456951413090

523600040013090

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 68033

405142257405142208=


72087366726

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

03343125324

5236000

4811253245622604

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

73154306624

523600024

6703066245622604

24

=sdotsdot

==

=sdotsdot

==

502412

24===

Hrρ


Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDZq

QukAr

o

o

o

ro

171min701107720min243720106

393171670720830

260

602239613932

12513968

72010

3620

17671660172010

7200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDZq

QukAr

qgkCBA

ro

5335601110

3200

113110

306242206

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

==sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 19891890

17asymp===

α


10400320072006240006010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

601

min7670min40

30

3200min6

830min506242206

202003805080

908

1060

72006072

2

2

32

1

1

1

1

===

===

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoDrHrZ

qnGp

qQ

vozilaZq

QukAr

o

o

o

o

272min13685020851min9090205

61527217151670

520

502228116706155

776762811969

9020

6030

5474779020

6200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp=sdot

=sdot

=

=sdot

=sdot

==

asymp=sdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozZq

QukAr

qgkCBA

o

32137785020

4200

85020

405242207

2

22

2

asymp=sdotsdot

=sdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 62659505

asymp===α


10400420062005200005010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

20670min40

min8171min70

40

4200min5

670min405242207

30300014070

9509

2050

620096120

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

106122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Поставка

C 105 km D

175km 135km

B

400km

A

Решење

vozArAi 17880

15===

α


44406425341872

22

21


γ



htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

25355040

min120min5

min5min10

88057min450

1624

8806501872

24

630

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZq

QukArAr

o

o

o

o

2min120761min6105880245

31min7865024562min1566502410

66727613162

73240400

50135

35105

25175

40400

864757667732

802886472416

15865024

1872

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

=sdotsdot

=sdotsdot

==

γτγτγτ

γ



35km 45km

B

80km

A

Решење

vozArAi 48537803

asymp===α


6243352317802065205624332772

22

21


γ



voztitutitu

htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

35504530

min30min8min10min3

78050min30

1620

7808502772

52

1062

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrttoHrZ

vozilaDZq

QukArAr

o

o

o

ro

50min30082min8124780208

832min1708502010850min51850203

26650082832850

6483080

4545

5065

3535

3080

41550266648

1041415

16

314352185020

2772

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

γτγτγτ

γ


Поставка

C 80 km D

150km 95km

B

280km

A

Решење

vozArAi 87790

7asymp===

α

tQukQukQuk 71702570460021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

60555030

min92min120

min8min10

904min240

1622

820970

25704600

80

1292

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

712min36162820229852min72170970228

563min4213970221012117122852563

522430280

60150

5580

5095

30280

6439413115224

32293264398016

44543282022

2570

77463297022

4600

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ



Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ



Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


Решење


Di=60dana

1802

7016

30min2

650214257

21420526

8046800

46

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituituituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

780min846902627822780

33530

8022118782335

2971118

16

141144629026

304203042065046800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 9026

650214257650214205=


vozilaArAi 1851780

14asymp===



tkmKtQukUuk

363248346142970263662903363248330420

85032268807264966

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 97026

7021425770214205=


660118335

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

38488161446

85032268

161614463662903

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

15194601824

8503226824

4326018243662903

24

=sdotsdot

==

=sdotsdot

==

6702416

24===

Hrρ


Решење


Di=50dana

1603

9014

40min3

750512256

51220536

6036800

36

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

421min32857903634243421

340

60224274243

2881427

14

13471336279036

276002760075036800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 79036

750512256750512205=


vozilaArAi 22662160

13asymp===



tkmKtQukUuk

243167436132940362459274243167427600

43556454602459274

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 94026

9051225690512205=


404273

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

80542141336

43556454

0491413362459274

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

71134502224

4355645424

2525022242459274

24

=sdotsdot

==

=sdotsdot

==

5802414

24===

Hrρ


Решење


Di=90dana

1903

8016

40min8

440512207

51220532

4016800

72

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

32min2413854032835332

240

402237352

219237

16

397272254032

7392739244016800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 54032

440512207440512205=


vozilaArAi 333390

3asymp===



tkmKtQukUuk

7613685723299032762107776136857392

4843110407621077

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 99032

8051220780512205=


27037

2===

totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

9624316372

4843110

16163727621077

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

6416272324

484311024

074723247621077

24

=sdotsdot

==

=sdotsdot

==

6702416

24===

Hrρ


Решење


Di=30dana

90904

4012

30min12

5505142257

514220833

40023800

24

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoDrHrZ

vozilaZq

QukAA

tgkVQuk

o

orr

26min243729403312210426

67263040022

87362106726

881787362412

537552894033

130901309055023800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 94033

55051422575505142208=



53asymp===


tArZoqQuktQukQukQuk

tkmKtQukUuk

56951453868033562260456951413090

523600040013090

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 68033

405142257405142208=


72087366726

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

03343125324

5236000

4811253245622604

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

73154306624

523600024

6703066245622604

24

=sdotsdot

==

=sdotsdot

==

502412

24===

Hrρ


Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDZq

QukAr

o

o

o

ro

171min701107720min243720106

393171670720830

260

602239613932

12513968

72010

3620

17671660172010

7200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDZq

QukAr

qgkCBA

ro

5335601110

3200

113110

306242206

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

==sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 19891890

17asymp===

α


10400320072006240006010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

601

min7670min40

30

3200min6

830min506242206

202003805080

908

1060

72006072

2

2

32

1

1

1

1

===

===

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoDrHrZ

qnGp

qQ

vozilaZq

QukAr

o

o

o

o

272min13685020851min9090205

61527217151670

520

502228116706155

776762811969

9020

6030

5474779020

6200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp=sdot

=sdot

=

=sdot

=sdot

==

asymp=sdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozZq

QukAr

qgkCBA

o

32137785020

4200

85020

405242207

2

22

2

asymp=sdotsdot

=sdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 62659505

asymp===α


10400420062005200005010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

20670min40

min8171min70

40

4200min5

670min405242207

30300014070

9509

2050

620096120

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

106122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Поставка

C 105 km D

175km 135km

B

400km

A

Решење

vozArAi 17880

15===

α


44406425341872

22

21


γ



htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

25355040

min120min5

min5min10

88057min450

1624

8806501872

24

630

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZq

QukArAr

o

o

o

o

2min120761min6105880245

31min7865024562min1566502410

66727613162

73240400

50135

35105

25175

40400

864757667732

802886472416

15865024

1872

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

=sdotsdot

=sdotsdot

==

γτγτγτ

γ



35km 45km

B

80km

A

Решење

vozArAi 48537803

asymp===α


6243352317802065205624332772

22

21


γ



voztitutitu

htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

35504530

min30min8min10min3

78050min30

1620

7808502772

52

1062

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrttoHrZ

vozilaDZq

QukArAr

o

o

o

ro

50min30082min8124780208

832min1708502010850min51850203

26650082832850

6483080

4545

5065

3535

3080

41550266648

1041415

16

314352185020

2772

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

γτγτγτ

γ


Поставка

C 80 km D

150km 95km

B

280km

A

Решење

vozArAi 87790

7asymp===

α

tQukQukQuk 71702570460021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

60555030

min92min120

min8min10

904min240

1622

820970

25704600

80

1292

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

712min36162820229852min72170970228

563min4213970221012117122852563

522430280

60150

5580

5095

30280

6439413115224

32293264398016

44543282022

2570

77463297022

4600

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ



Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ



Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


Решење


Di=50dana

1603

9014

40min3

750512256

51220536

6036800

36

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

421min32857903634243421

340

60224274243

2881427

14

13471336279036

276002760075036800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 79036

750512256750512205=


vozilaArAi 22662160

13asymp===



tkmKtQukUuk

243167436132940362459274243167427600

43556454602459274

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 94026

9051225690512205=


404273

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

80542141336

43556454

0491413362459274

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

71134502224

4355645424

2525022242459274

24

=sdotsdot

==

=sdotsdot

==

5802414

24===

Hrρ


Решење


Di=90dana

1903

8016

40min8

440512207

51220532

4016800

72

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

32min2413854032835332

240

402237352

219237

16

397272254032

7392739244016800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 54032

440512207440512205=


vozilaArAi 333390

3asymp===



tkmKtQukUuk

7613685723299032762107776136857392

4843110407621077

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 99032

8051220780512205=


27037

2===

totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

9624316372

4843110

16163727621077

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

6416272324

484311024

074723247621077

24

=sdotsdot

==

=sdotsdot

==

6702416

24===

Hrρ


Решење


Di=30dana

90904

4012

30min12

5505142257

514220833

40023800

24

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoDrHrZ

vozilaZq

QukAA

tgkVQuk

o

orr

26min243729403312210426

67263040022

87362106726

881787362412

537552894033

130901309055023800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 94033

55051422575505142208=



53asymp===


tArZoqQuktQukQukQuk

tkmKtQukUuk

56951453868033562260456951413090

523600040013090

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 68033

405142257405142208=


72087366726

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

03343125324

5236000

4811253245622604

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

73154306624

523600024

6703066245622604

24

=sdotsdot

==

=sdotsdot

==

502412

24===

Hrρ


Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDZq

QukAr

o

o

o

ro

171min701107720min243720106

393171670720830

260

602239613932

12513968

72010

3620

17671660172010

7200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDZq

QukAr

qgkCBA

ro

5335601110

3200

113110

306242206

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

==sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 19891890

17asymp===

α


10400320072006240006010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

601

min7670min40

30

3200min6

830min506242206

202003805080

908

1060

72006072

2

2

32

1

1

1

1

===

===

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoDrHrZ

qnGp

qQ

vozilaZq

QukAr

o

o

o

o

272min13685020851min9090205

61527217151670

520

502228116706155

776762811969

9020

6030

5474779020

6200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp=sdot

=sdot

=

=sdot

=sdot

==

asymp=sdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozZq

QukAr

qgkCBA

o

32137785020

4200

85020

405242207

2

22

2

asymp=sdotsdot

=sdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 62659505

asymp===α


10400420062005200005010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

20670min40

min8171min70

40

4200min5

670min405242207

30300014070

9509

2050

620096120

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

106122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Поставка

C 105 km D

175km 135km

B

400km

A

Решење

vozArAi 17880

15===

α


44406425341872

22

21


γ



htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

25355040

min120min5

min5min10

88057min450

1624

8806501872

24

630

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZq

QukArAr

o

o

o

o

2min120761min6105880245

31min7865024562min1566502410

66727613162

73240400

50135

35105

25175

40400

864757667732

802886472416

15865024

1872

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

=sdotsdot

=sdotsdot

==

γτγτγτ

γ



35km 45km

B

80km

A

Решење

vozArAi 48537803

asymp===α


6243352317802065205624332772

22

21


γ



voztitutitu

htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

35504530

min30min8min10min3

78050min30

1620

7808502772

52

1062

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrttoHrZ

vozilaDZq

QukArAr

o

o

o

ro

50min30082min8124780208

832min1708502010850min51850203

26650082832850

6483080

4545

5065

3535

3080

41550266648

1041415

16

314352185020

2772

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

γτγτγτ

γ


Поставка

C 80 km D

150km 95km

B

280km

A

Решење

vozArAi 87790

7asymp===

α

tQukQukQuk 71702570460021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

60555030

min92min120

min8min10

904min240

1622

820970

25704600

80

1292

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

712min36162820229852min72170970228

563min4213970221012117122852563

522430280

60150

5580

5095

30280

6439413115224

32293264398016

44543282022

2570

77463297022

4600

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ



Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ



Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


Решење


Di=90dana

1903

8016

40min8

440512207

51220532

4016800

72

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoHrZ

vozilaDZq

QukAA

tgkVQuk

o

rorr

32min2413854032835332

240

402237352

219237

16

397272254032

7392739244016800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 54032

440512207440512205=


vozilaArAi 333390

3asymp===



tkmKtQukUuk

7613685723299032762107776136857392

4843110407621077

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 99032

8051220780512205=


27037

2===

totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

9624316372

4843110

16163727621077

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

6416272324

484311024

074723247621077

24

=sdotsdot

==

=sdotsdot

==

6702416

24===

Hrρ


Решење


Di=30dana

90904

4012

30min12

5505142257

514220833

40023800

24

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoDrHrZ

vozilaZq

QukAA

tgkVQuk

o

orr

26min243729403312210426

67263040022

87362106726

881787362412

537552894033

130901309055023800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 94033

55051422575505142208=



53asymp===


tArZoqQuktQukQukQuk

tkmKtQukUuk

56951453868033562260456951413090

523600040013090

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 68033

405142257405142208=


72087366726

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

03343125324

5236000

4811253245622604

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

73154306624

523600024

6703066245622604

24

=sdotsdot

==

=sdotsdot

==

502412

24===

Hrρ


Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDZq

QukAr

o

o

o

ro

171min701107720min243720106

393171670720830

260

602239613932

12513968

72010

3620

17671660172010

7200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDZq

QukAr

qgkCBA

ro

5335601110

3200

113110

306242206

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

==sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 19891890

17asymp===

α


10400320072006240006010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

601

min7670min40

30

3200min6

830min506242206

202003805080

908

1060

72006072

2

2

32

1

1

1

1

===

===

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoDrHrZ

qnGp

qQ

vozilaZq

QukAr

o

o

o

o

272min13685020851min9090205

61527217151670

520

502228116706155

776762811969

9020

6030

5474779020

6200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp=sdot

=sdot

=

=sdot

=sdot

==

asymp=sdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozZq

QukAr

qgkCBA

o

32137785020

4200

85020

405242207

2

22

2

asymp=sdotsdot

=sdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 62659505

asymp===α


10400420062005200005010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

20670min40

min8171min70

40

4200min5

670min405242207

30300014070

9509

2050

620096120

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

106122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Поставка

C 105 km D

175km 135km

B

400km

A

Решење

vozArAi 17880

15===

α


44406425341872

22

21


γ



htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

25355040

min120min5

min5min10

88057min450

1624

8806501872

24

630

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZq

QukArAr

o

o

o

o

2min120761min6105880245

31min7865024562min1566502410

66727613162

73240400

50135

35105

25175

40400

864757667732

802886472416

15865024

1872

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

=sdotsdot

=sdotsdot

==

γτγτγτ

γ



35km 45km

B

80km

A

Решење

vozArAi 48537803

asymp===α


6243352317802065205624332772

22

21


γ



voztitutitu

htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

35504530

min30min8min10min3

78050min30

1620

7808502772

52

1062

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrttoHrZ

vozilaDZq

QukArAr

o

o

o

ro

50min30082min8124780208

832min1708502010850min51850203

26650082832850

6483080

4545

5065

3535

3080

41550266648

1041415

16

314352185020

2772

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

γτγτγτ

γ


Поставка

C 80 km D

150km 95km

B

280km

A

Решење

vozArAi 87790

7asymp===

α

tQukQukQuk 71702570460021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

60555030

min92min120

min8min10

904min240

1622

820970

25704600

80

1292

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

712min36162820229852min72170970228

563min4213970221012117122852563

522430280

60150

5580

5095

30280

6439413115224

32293264398016

44543282022

2570

77463297022

4600

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ



Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ



Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


Решење


Di=30dana

90904

4012

30min12

5505142257

514220833

40023800

24

2

32

1

31

1

3

=prime===

====


==

=

=

αα

τ

thtui

mtgkhHr

hkmVstuimtgk

CBACBAtqkmKtmV

danaDr

hquituihtuituitui

hVsKttwo

htuitwoto

obrtatoDrHrZ

vozilaZq

QukAA

tgkVQuk

o

orr

26min243729403312210426

67263040022

87362106726

881787362412

537552894033

130901309055023800

111

21

1

1

11

11


=sdot

==

=+=+=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

==

=sdot=sdot=

γτ

γ

qgkCBAgkCBA

qgkVpgkVv 1111


=sdot+sdot

=γ 94033

55051422575505142208=



53asymp===


tArZoqQuktQukQukQuk

tkmKtQukUuk

56951453868033562260456951413090

523600040013090

22

21

1


=sdot=sdot=

γ

qgkCBAgkCBA

qgkVpgkVv 2222


=sdot+sdot

=γ 68033

405142257405142208=


72087366726

===totwoδ 1

22

1

1 =sdotsdotsdotsdot

==ZoKtArZoKtAr

AKAKtβ

htkmAHUukW

htAHQ

W

rU

r

ukQ

03343125324

5236000

4811253245622604

=sdotsdot

==prime

=sdotsdot

==prime

htkmADiUukW

htADiQ

W

U

ukQ

73154306624

523600024

6703066245622604

24

=sdotsdot

==

=sdotsdot

==

502412

24===

Hrρ


Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDZq

QukAr

o

o

o

ro

171min701107720min243720106

393171670720830

260

602239613932

12513968

72010

3620

17671660172010

7200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDZq

QukAr

qgkCBA

ro

5335601110

3200

113110

306242206

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

==sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 19891890

17asymp===

α


10400320072006240006010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

601

min7670min40

30

3200min6

830min506242206

202003805080

908

1060

72006072

2

2

32

1

1

1

1

===

===

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoDrHrZ

qnGp

qQ

vozilaZq

QukAr

o

o

o

o

272min13685020851min9090205

61527217151670

520

502228116706155

776762811969

9020

6030

5474779020

6200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp=sdot

=sdot

=

=sdot

=sdot

==

asymp=sdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozZq

QukAr

qgkCBA

o

32137785020

4200

85020

405242207

2

22

2

asymp=sdotsdot

=sdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 62659505

asymp===α


10400420062005200005010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

20670min40

min8171min70

40

4200min5

670min405242207

30300014070

9509

2050

620096120

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

106122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Поставка

C 105 km D

175km 135km

B

400km

A

Решење

vozArAi 17880

15===

α


44406425341872

22

21


γ



htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

25355040

min120min5

min5min10

88057min450

1624

8806501872

24

630

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZq

QukArAr

o

o

o

o

2min120761min6105880245

31min7865024562min1566502410

66727613162

73240400

50135

35105

25175

40400

864757667732

802886472416

15865024

1872

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

=sdotsdot

=sdotsdot

==

γτγτγτ

γ



35km 45km

B

80km

A

Решење

vozArAi 48537803

asymp===α


6243352317802065205624332772

22

21


γ



voztitutitu

htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

35504530

min30min8min10min3

78050min30

1620

7808502772

52

1062

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrttoHrZ

vozilaDZq

QukArAr

o

o

o

ro

50min30082min8124780208

832min1708502010850min51850203

26650082832850

6483080

4545

5065

3535

3080

41550266648

1041415

16

314352185020

2772

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

γτγτγτ

γ


Поставка

C 80 km D

150km 95km

B

280km

A

Решење

vozArAi 87790

7asymp===

α

tQukQukQuk 71702570460021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

60555030

min92min120

min8min10

904min240

1622

820970

25704600

80

1292

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

712min36162820229852min72170970228

563min4213970221012117122852563

522430280

60150

5580

5095

30280

6439413115224

32293264398016

44543282022

2570

77463297022

4600

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ



Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ



Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDZq

QukAr

o

o

o

ro

171min701107720min243720106

393171670720830

260

602239613932

12513968

72010

3620

17671660172010

7200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDZq

QukAr

qgkCBA

ro

5335601110

3200

113110

306242206

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

==sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 19891890

17asymp===

α


10400320072006240006010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

601

min7670min40

30

3200min6

830min506242206

202003805080

908

1060

72006072

2

2

32

1

1

1

1

===

===

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoDrHrZ

qnGp

qQ

vozilaZq

QukAr

o

o

o

o

272min13685020851min9090205

61527217151670

520

502228116706155

776762811969

9020

6030

5474779020

6200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp=sdot

=sdot

=

=sdot

=sdot

==

asymp=sdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozZq

QukAr

qgkCBA

o

32137785020

4200

85020

405242207

2

22

2

asymp=sdotsdot

=sdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 62659505

asymp===α


10400420062005200005010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

20670min40

min8171min70

40

4200min5

670min405242207

30300014070

9509

2050

620096120

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

106122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Поставка

C 105 km D

175km 135km

B

400km

A

Решење

vozArAi 17880

15===

α


44406425341872

22

21


γ



htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

25355040

min120min5

min5min10

88057min450

1624

8806501872

24

630

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZq

QukArAr

o

o

o

o

2min120761min6105880245

31min7865024562min1566502410

66727613162

73240400

50135

35105

25175

40400

864757667732

802886472416

15865024

1872

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

=sdotsdot

=sdotsdot

==

γτγτγτ

γ



35km 45km

B

80km

A

Решење

vozArAi 48537803

asymp===α


6243352317802065205624332772

22

21


γ



voztitutitu

htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

35504530

min30min8min10min3

78050min30

1620

7808502772

52

1062

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrttoHrZ

vozilaDZq

QukArAr

o

o

o

ro

50min30082min8124780208

832min1708502010850min51850203

26650082832850

6483080

4545

5065

3535

3080

41550266648

1041415

16

314352185020

2772

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

γτγτγτ

γ


Поставка

C 80 km D

150km 95km

B

280km

A

Решење

vozArAi 87790

7asymp===

α

tQukQukQuk 71702570460021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

60555030

min92min120

min8min10

904min240

1622

820970

25704600

80

1292

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

712min36162820229852min72170970228

563min4213970221012117122852563

522430280

60150

5580

5095

30280

6439413115224

32293264398016

44543282022

2570

77463297022

4600

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ



Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ



Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoDrHrZ

qnGp

qQ

vozilaZq

QukAr

o

o

o

o

272min13685020851min9090205

61527217151670

520

502228116706155

776762811969

9020

6030

5474779020

6200

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp=sdot

=sdot

=

=sdot

=sdot

==

asymp=sdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozZq

QukAr

qgkCBA

o

32137785020

4200

85020

405242207

2

22

2

asymp=sdotsdot

=sdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 62659505

asymp===α


10400420062005200005010400

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKt

tQukdanaDdanaD

r

i

20670min40

min8171min70

40

4200min5

670min405242207

30300014070

9509

2050

620096120

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

106122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Поставка

C 105 km D

175km 135km

B

400km

A

Решење

vozArAi 17880

15===

α


44406425341872

22

21


γ



htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

25355040

min120min5

min5min10

88057min450

1624

8806501872

24

630

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZq

QukArAr

o

o

o

o

2min120761min6105880245

31min7865024562min1566502410

66727613162

73240400

50135

35105

25175

40400

864757667732

802886472416

15865024

1872

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

=sdotsdot

=sdotsdot

==

γτγτγτ

γ



35km 45km

B

80km

A

Решење

vozArAi 48537803

asymp===α


6243352317802065205624332772

22

21


γ



voztitutitu

htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

35504530

min30min8min10min3

78050min30

1620

7808502772

52

1062

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrttoHrZ

vozilaDZq

QukArAr

o

o

o

ro

50min30082min8124780208

832min1708502010850min51850203

26650082832850

6483080

4545

5065

3535

3080

41550266648

1041415

16

314352185020

2772

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

γτγτγτ

γ


Поставка

C 80 km D

150km 95km

B

280km

A

Решење

vozArAi 87790

7asymp===

α

tQukQukQuk 71702570460021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

60555030

min92min120

min8min10

904min240

1622

820970

25704600

80

1292

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

712min36162820229852min72170970228

563min4213970221012117122852563

522430280

60150

5580

5095

30280

6439413115224

32293264398016

44543282022

2570

77463297022

4600

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ



Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ



Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

106122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

asymp=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Поставка

C 105 km D

175km 135km

B

400km

A

Решење

vozArAi 17880

15===

α


44406425341872

22

21


γ



htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

25355040

min120min5

min5min10

88057min450

1624

8806501872

24

630

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZq

QukArAr

o

o

o

o

2min120761min6105880245

31min7865024562min1566502410

66727613162

73240400

50135

35105

25175

40400

864757667732

802886472416

15865024

1872

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

=sdotsdot

=sdotsdot

==

γτγτγτ

γ



35km 45km

B

80km

A

Решење

vozArAi 48537803

asymp===α


6243352317802065205624332772

22

21


γ



voztitutitu

htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

35504530

min30min8min10min3

78050min30

1620

7808502772

52

1062

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrttoHrZ

vozilaDZq

QukArAr

o

o

o

ro

50min30082min8124780208

832min1708502010850min51850203

26650082832850

6483080

4545

5065

3535

3080

41550266648

1041415

16

314352185020

2772

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

γτγτγτ

γ


Поставка

C 80 km D

150km 95km

B

280km

A

Решење

vozArAi 87790

7asymp===

α

tQukQukQuk 71702570460021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

60555030

min92min120

min8min10

904min240

1622

820970

25704600

80

1292

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

712min36162820229852min72170970228

563min4213970221012117122852563

522430280

60150

5580

5095

30280

6439413115224

32293264398016

44543282022

2570

77463297022

4600

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ



Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ



Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


Решење



Поставка


hqitihqiti

htitutitutui

hVsKttw

htostuitwto

obrttoHrZ

qnGp

qQ

vozilaDrZq

QukAr

o

o

o

o

22min1321226331min0880910224

864221331330

54010022

3611518645

10613611

12

91022

80250

453120191022

8300

222

111

2211

1

11

1

11


=+++=+++=

=sdot

==

=++=++=

asymp===

=sdot

=sdot

==

asymp=sdotsdotsdot

=sdotsdotsdot

=

γτγτ

γ

γ

vozDrZq

QukAr

qgkCBA

o

21621201122

5700

122

504242208

2

22

2

asymp=sdotsdotsdot

=sdotsdotsdot

=

=sdotsdotsdot

=sdotsdotsdot

=

γ

γ

vozArAi 580

4===

α


1400057008300140000010014000

21

1

=+=+==sdot=sdot=


A B

hkmVshtos

tihvoztu

mtgk

tQukti

hvoztuCBA

tkgGpmcba

hHrtqkmKttQuk

danaDdanaD

r

i

4051min90

min61min60

50

5700min4

330min204242208

250250014060

8012

22100

8300120150

2

2

32

1

1

1

1

===

===

=

==

==sdotsdot=sdotsdot

==sdotsdot=sdotsdot

==

===

==

τ

τ

α



Поставка

C 105 km D

175km 135km

B

400km

A

Решење

vozArAi 17880

15===

α


44406425341872

22

21


γ



htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

25355040

min120min5

min5min10

88057min450

1624

8806501872

24

630

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZq

QukArAr

o

o

o

o

2min120761min6105880245

31min7865024562min1566502410

66727613162

73240400

50135

35105

25175

40400

864757667732

802886472416

15865024

1872

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

=sdotsdot

=sdotsdot

==

γτγτγτ

γ



35km 45km

B

80km

A

Решење

vozArAi 48537803

asymp===α


6243352317802065205624332772

22

21


γ



voztitutitu

htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

35504530

min30min8min10min3

78050min30

1620

7808502772

52

1062

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrttoHrZ

vozilaDZq

QukArAr

o

o

o

ro

50min30082min8124780208

832min1708502010850min51850203

26650082832850

6483080

4545

5065

3535

3080

41550266648

1041415

16

314352185020

2772

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

γτγτγτ

γ


Поставка

C 80 km D

150km 95km

B

280km

A

Решење

vozArAi 87790

7asymp===

α

tQukQukQuk 71702570460021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

60555030

min92min120

min8min10

904min240

1622

820970

25704600

80

1292

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

712min36162820229852min72170970228

563min4213970221012117122852563

522430280

60150

5580

5095

30280

6439413115224

32293264398016

44543282022

2570

77463297022

4600

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ



Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ



Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


Поставка

C 105 km D

175km 135km

B

400km

A

Решење

vozArAi 17880

15===

α


44406425341872

22

21


γ



htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

25355040

min120min5

min5min10

88057min450

1624

8806501872

24

630

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZq

QukArAr

o

o

o

o

2min120761min6105880245

31min7865024562min1566502410

66727613162

73240400

50135

35105

25175

40400

864757667732

802886472416

15865024

1872

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

=sdotsdot

=sdotsdot

==

γτγτγτ

γ



35km 45km

B

80km

A

Решење

vozArAi 48537803

asymp===α


6243352317802065205624332772

22

21


γ



voztitutitu

htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

35504530

min30min8min10min3

78050min30

1620

7808502772

52

1062

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrttoHrZ

vozilaDZq

QukArAr

o

o

o

ro

50min30082min8124780208

832min1708502010850min51850203

26650082832850

6483080

4545

5065

3535

3080

41550266648

1041415

16

314352185020

2772

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

γτγτγτ

γ


Поставка

C 80 km D

150km 95km

B

280km

A

Решење

vozArAi 87790

7asymp===

α

tQukQukQuk 71702570460021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

60555030

min92min120

min8min10

904min240

1622

820970

25704600

80

1292

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

712min36162820229852min72170970228

563min4213970221012117122852563

522430280

60150

5580

5095

30280

6439413115224

32293264398016

44543282022

2570

77463297022

4600

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ



Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ



Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα



35km 45km

B

80km

A

Решење

vozArAi 48537803

asymp===α


6243352317802065205624332772

22

21


γ



voztitutitu

htoshHrtq

tQukdanaDr

danaDdanaD

CB

DC

DB

BA

p

i

35504530

min30min8min10min3

78050min30

1620

7808502772

52

1062

2

2

1

1

2

1

1

====

=====

===

===

==

==

minus

minus

minus

minus

τττα

γγ

htihqutu

hqitihqutu

htitutitutui

htw

htostuitwto

obrttoHrZ

vozilaDZq

QukArAr

o

o

o

ro

50min30082min8124780208

832min1708502010850min51850203

26650082832850

6483080

4545

5065

3535

3080

41550266648

1041415

16

314352185020

2772

2

222

111

111

2211

1

11



=+++=+++=

=++++=

=++=++=

asymp===

asymp=sdotsdotsdot

=sdotsdotsdot

==

γτγτγτ

γ


Поставка

C 80 km D

150km 95km

B

280km

A

Решење

vozArAi 87790

7asymp===

α

tQukQukQuk 71702570460021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

60555030

min92min120

min8min10

904min240

1622

820970

25704600

80

1292

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

712min36162820229852min72170970228

563min4213970221012117122852563

522430280

60150

5580

5095

30280

6439413115224

32293264398016

44543282022

2570

77463297022

4600

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ



Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ



Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


Поставка

C 80 km D

150km 95km

B

280km

A

Решење

vozArAi 87790

7asymp===

α

tQukQukQuk 71702570460021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

60555030

min92min120

min8min10

904min240

1622

820970

25704600

80

1292

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

712min36162820229852min72170970228

563min4213970221012117122852563

522430280

60150

5580

5095

30280

6439413115224

32293264398016

44543282022

2570

77463297022

4600

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ



Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ



Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


Поставка

C 80 km D

100km 65km

B

150km

A

Решење

vozArAi 89578807

asymp===α

tQukQukQuk 148008300650021 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDrdanaDdanaD

CB

DC

DB

BA

p

i

30503060

min102min120

min12min9

8802min120

1620

980870

83006500

10020

120

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

273min1969802010483min82088702012612min6156870209

36112732483612

11260

15030

1005080

3065

60150

462523611112

6384624625

10016

77266398020

8300

69356387020

6500

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ



Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


Поставка

C 90 km D

130km 85km

B

250km

A

Решење

vozArAi 336532980

32asymp===

α

tQukQukQuk 91645232393221 =+=+=



tihvoztu

titu

htoshHrtq

tQuktQuk

danaDr

danaDdanaD

CB

DC

DB

BA

p

i

20453040

min73min180

min9min15

9805min300

1618

920770

52323932

22

830

2

2

1

1

2

1

2

1

====

===

===

===

===

==

=

==

minus

minus

minus

minus

τ

ττα

γγ

hqitihqitihqutu

htitutitutui

htw

htostuitwto

obrtatoDrHrZ

vozilaZoq

QukAr

vozilaZq

QukAr

o

o

o

o

931min92115920187082min74124770189473min92077701815

48109313082473

332140250

3085

4590

20130

40250

8136548108321

1056981362216

3259311092018

5232

283728977018

3932

222

111

111

2211

2

22

1

11


=+++=+++=

=++++=

=++=++=

asymp=sdot

=sdot

=

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

γτγτγτ

γ

γ






huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα





huntituhtitutui

hVsKt

tw

htoptwto

obrtatoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

071min64232142071071

83758

1227228083028372

28

16

10220

2065

1300

130032200

8320000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

===

====

===

=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)5808301227(2)08302142(58110 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot


Решење


hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

580830min5

min216

014205757407475

580581227

58320000

65

1

===

===

===

===

===




vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα



vožnjinV

QukZburbur

100021350

7350000=

sdot=

sdot=λ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZ

Ar

vožnjiDrZZ

o

o

dn

dn

751min1055215375171

91840

21782225917029182

2731259

16

52

10

10100

1000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

===

===

τ

λ

λλ

=⎥

⎦

⎤⎢⎣

⎡sdot+sdot+sdot

+sdot=)(2)2(1


)401702178(2)170253(4015 asymp=⎥⎦

⎤⎢⎣

⎡sdot+

sdot+sdot+sdot





hkmVshtop

buriuhHr

mxxAxBxCmcmH

mcmRkmKt

tqlQuk

danaDr

40170min10

min516

014206696706769

800802178

88320000

100

1

===

===

===

===

===

ττ


=P

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

45130min8

min416

01420880808080

15010

555000055

1

===

===

=====

==

==

ττ


huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα

huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

2min120430422

574015022

7671302572

2062767

16

428

836855460

460246030402

5550000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)40130150(2)13024(4014 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKt

tw

htoptwto

obrttoHrZo

tegljačeZoZ

AtAr

vožnjiDrZZ

vožnjinV

QukZ

o

o

dn

dn

burbur

51min9033035151

33133020022

531310233132

11815313

16

131

13

13511280

1001

100130308

9250000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

====

asymp===

=sdot

=sdot

=

τ

λ

λλ

λ

hkmVshtop

buriuhHr

mxxAxBxCmcmHmcmR

kmKttq

lQukdanaDr

30110min6

min316

01420780807070

2009

925000080

1

===

===

=====

==

==


=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)3010200(2)1023(30113 asymp=⎥⎦

⎤⎢⎣

⎡sdot+sdot

sdot+sdot+sdot





huntituhtitutui

hVsKttw

htoptwto

obrtatoHrZo

tegljačeZoZAtAr

vožnjiDrZZ

vožnjanV

QukZ

o

o

dn

dn

burbur

11min66233221111

845012022

5102842

26158

35225

512592471

4717347033309

4800000

1

==sdot=sdot===+=+=

=sdot

==

=sdot+=sdot+=

asymp===

asymp====

asymp===

asymp=sdot

=sdot

=

τ

λ

λλ

λ

=⎥⎦

⎤⎢⎣


+sdot=)(2)2(1


)5010120(2)10222(5013 asymp=⎥⎦

⎤⎢⎣


+sdot

hkmVshtopburiu

hHrmxxAxBxC

mcmHmcmR

kmKttq

lQukdanaDr

5010min6

min216

0142087607672072

12012

480000092

1

===

===

=====

==

==



Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


Поставка

Решење


min6241360

max60

max

min57876060

133133190

3591maxmax

7716818090

870

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolp

PhAh

sma

sma

ηγ

ηγ

180

9015120

min5min17010

92010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1613(3max891

381

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdn

Ph

putHrPhP

hputHrPdn

Phsr

hputPhsrPh n

8704869381077315120

maxmax

1077333591maxmaxmax

18908

151203591911890max

asymp=minus

minus=

minus

minus=

=sdot=sdot=

===

=sdot=sdot= η

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

vozIwtoAr

vozIwtoAr

16815624

73max

max

9528578

73

asymp===

asymp===

min601201022

min06735517092602

==sdot

==


hVsKltw

tktptsitwto

o

o


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


km

k 1332 1337

9

8

7

6

5

4

3

2

1 1408 1413

P 1300 1330 1400 1430 h


Поставка

Pешење

533117092

602

=sdot+=sdot+ tsitwo

190

10018000

min10min33020

72515

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1612(4max16

714

71

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

86333862416765218000

maxmax

765241913maxmaxmax

112516

18000191351912711125max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min125

60max

60max

min106

6060

578441100

1913maxmax

66457190100

863

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min7221251522

min976296101033072722

==sdot

==


hVsKltw

tktptsitwto

o

o



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα



km

k 1238 1248

7

6

5

4

3

2

1 1327 1337

P 1200 1230 1300 1330 h

313833072

722

=sdot+=sdot+ tsitwo

vozIwtoAr

vozIwtoAr

80881297

maxmax

10791097

asymp===

asymp===


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


Поставка

Pешење


180

12022000

min10min5030

83025

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min545082

1002

=sdot+=sdot+ tsitwo

)1713(4max16

913

81

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

96333962416

1045222000maxmax

1045242613maxmaxmax

137516

22000261352612911375max

asymp=minusminus

=minusminus

=

=sdot=sdot=

===

asymp=sdot=sdot= η

min578760

max60

max

min1066060

723731120

2613maxmax

65658180120

963

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolp

PhAh

hpolpPh

Ah

sma

sma

ηγ

ηγ

min10067130

2522min128101050821002

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

159314578

128max

max

1381210

128

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

maxnapolnapol

Iw

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα

km

k 1354 1404

7

6

5

4

3

2

1 1458 1508

P 1300 1400 1500 1600 h


Поставка

Решење

min8622160

max60max

min3206060

21162132190

4380maxmax

202820228090

3212

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

180

9029200

min15min33020

93012

maxmaxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

)1714(3max821

3222

max

hhHrhHr

n

sm

sm

minus===

==

ηηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

3212381314029200

maxmax

1314034380maxmaxmax

36508

292004380213650max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


km

k 527 542

9

8

7

6

5

4

3

2

1 609 624

P 500 530 600 630 h

vozIwtoAr

vozIwtoAr

293729862

84max

max

283

84

asymp===

===

min488030

1222min849483151533092482

==sdot

==


hVsKltw

tktptsitwto

o

o

min27972633092

482



Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


Поставка

Pешење


170

10032000

min10min17010

72010

max

maxmaxmax

maxmax ====

======

====

====

aa

aa

mestapputPdn

tktpsts

ikmVskmKl

GRVArArIwIwAhAhPhPh

εγεγ

min31193117072

602


)1713(4max20

1252max

hhHrhHr

n

smsm

minus===

==η

ηη

hputHrHrPPdnPh

putHrPhP

hputHrPdnPhsr

hputPhsrPh n

1160420

1344032000maxmax

1344043360maxmaxmax

160020

320003360121600max

=minusminus

=minusminus

=

=sdot=sdot=

===

=sdot=sdot= η

min6241360

max60max

min57876060

134413521100

3360maxmax

76365270100

1160

maxmax

===

===

asymp=sdotsdot

=sdotsdot

=

asymp=sdotsdot

=sdotsdot

=

AhIw

AhIw

hpolpPhAh

hpolpPhAh

sma

sma

ηγ

ηγ

min601201022

min823882101017072602

==sdot

==


hVsKltw

tktptsitwto

o

o

vozIwtoAr

vozIwtoAr

187517614

82max

max

10579578

82

asymp===

asymp===

⎭⎬⎫

⎩⎨⎧

=min94min83

napolnapol

Iw⎭⎬⎫

⎩⎨⎧

=min58min45

maxnapolnapol

Iw

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα

km

k 1331 1341

7

6

5

4

3

2

1 1412 1422

P 1300 1330 1400 1430 h






LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VL

tVL

tVL

ttVL


2030

60middot422030

60middot152030

60middot24202030

60middot3020 +++++++++=Ot

htO 75min342222120 ==+=


obrtatHZoO

R 21275

12asymp===






86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα





86011196

42152430422430

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 471975

111===


Решење

903

908013

908013n

isr 321

n

1 =++

=++

=γ+γ+γ

=γ

=γsum

Kst 103

303

8616n

Kti==

++==λ km

7903830

4486168616

)(1

1 ==++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

570603

4830241 =sdot++

==sum

to = two + tuin

two = Vs


two = h9120

486416=

++++

to = h58368191560391 =+=sdot+

obrtatoVs

KpKnKnHr

Zo 4114583

2041015221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

448)908806116(44)(1



Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


Kt 1 = 4 km Q 1 = 04 t

Kt 2 = 6 km Q 2 = 07 t

Kt 3 = 10 km Q 3 = 08 t

Kt 4 = 7 km Q 4 = 12 t


РЕШЕЊЕ

890531

134321 =sdot

=sdot

+++=

qZoQQQQ

srγ

to = 652214512120294321 =+=+=+

++++tui

VsKpKtKtKtKt

h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


3040

60middot223040

60middot253040

60middot34303040

60middot4030 +++++++++=Ot

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα

htO 026min5361 ==


obrtatHZoO

R 3662535

16asymp===






79012196

22253440223440

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 120026

121===


Решење

8703

907013

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6711

38918=

++==λ

710868918

8918

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

530603

4035201 =sdot++

==sum


hVs

KpKpKtKtKttwo 631

3086891821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 5944223

3081116221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα

tkmiKtiqZodnUn

1260)908709118(85)(1



Kt 1 = 9 km Q 1 = 02 t

Kt 2 = 8 km Q 2 = 05 t

Kt 3 = 12 km Q 3 = 07 t

Kt 4 = 6 km Q 4 = 12 t


РЕШЕЊЕ

52051

217050204321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 45351

204612894321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα

4020

60middot324020

60middot234020

60middot14404020

60middot2040 +++++++++=Ot

htO 458min507 ==


obrtatHZoO

R 2661458

14asymp===






7408966

32231420321420

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 5310458

89===


Решење

7703

8060903

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 6715

3151220

=++

==λ

75088151220

151220

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

250603

2015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 153

208815122021321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα

obrtatoVs

KpKnKnHr

Zo 31339320

8412221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

1116)801560129020(103)(1



Kt 1 = 15 km Q 1 = 05 t

Kt 2 = 18 km Q 2 = 08 t

Kt 3 = 20 km Q 3 = 10 t

Kt 4 = 22 km Q 4 = 21 t


РЕШЕЊЕ

73061

120180504321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 97321

308222018154321 =+

++++=+

++++= h








LAB

А B

LAD LBC

LCD

D C

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα

Решење

iAS

DAUD

S

CDiC

S

BCUBiB

S

ABUAO t

VLt

VL

tVL

ttVLtt +++++++++=


1025

60middot381025

60middot281025

60middot25101025

60middot3310 +++++++++=Ot

htO 965min6357 ==


obrtatHZoO

R 2681965

10asymp===






77012496

38282533382533

==+++

++=

+++++

==DACDBCAB

DABCAB

LLLLLLL

KKtβ


hkmtKVo

e 8120965

124===


Решење

6303

4090603

3211 =++

=++

==sum γγγ

γγ

n

isr

n

kmnKtiKst 19

3141528

=++

==λ

7401010141528

141528

)(1

1 =++++

++=

+=

sum

sumn

n

KpiKti

Ktioβ

hn

tuitui

n

190603

1015101 =sdot++

==sum


hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα

hVs

KpKpKtKtKttwo 572

30101014152821321 =

++++=

++++=

obrtatoVs

KpKnKnHr

Zo 4793143

30101312221

asymp=

minusminus

=

minus+minus

=


tkmiKtiqZodnUn

81866)401490156028(134)(1



Kt 1 = 25 km Q 1 = 14 t

Kt 2 = 18 km Q 2 = 16 t

Kt 3 = 13 km Q 3 = 18 t

Kt 4 = 10 km Q 4 = 22 t


РЕШЕЊЕ

78091

228161414321 =sdot

+++=

sdot+++

=qZo

QQQQsrγ

htuiVs

KpKtKtKtKtto 350

309101318254321 =+

++++=+

++++=


























11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα












11014100

=sdot

=sdot

=


190009500

10011014

100=sdot

sdot=sdot

sdot=


54030100

=sdot

=sdot

=

kmlKmu

VmuPmu 100303000

1009100=

sdot=

sdot=


190009500

10054030

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

40000200006

=sdot

=sdot

=

tkmdinUk

KgCgNgTg 51

190009500

40000200006

=sdotsdot

=sdotsdot

=




kmdinKvCvTam 42

25000010500000

===

tkmdinUK

KvCvTam 21

190009500

25000010500000

=sdot=sdot=

kmdinKgodCrTor 11

5000055000

===





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα





РЕШЕЊЕ


two= =VsKo

VsKt12

two= 12020

20102

==sdot

h two=1 h

tui=tu + ti =8+12 = 20 min tui=6020

=033 h


Xu = =sdot

=sdot

=γsdotsdotτsdot

80830

totuAr

toquAr

3 mesta Xu= 3 mesta

Xi = ==sdot

=sdot

=γsdotsdotτsdot

80360

801230

totiAr

toqiAr



Iw= 6723080

Arto

== min

tkmdinUK

KgodCrTor 550

190009500

5000055000

=sdot=sdot=
























10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα





















10012100

=sdot

=sdot

=


2500010000

10010012

100=sdot

sdot=sdot

sdot=


500210100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002102800

1006100=

sdot=

sdot=


2500010000

100500210

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 3

30000150006

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 21

2500010000

40000200006

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα








РЕШЕЊЕ


two= =VsKo

VsKt12

two= h33130

202=

sdot h

tui=tu + ti =10+15 = 25 min tui=6025

=042 h


Xu = =sdot

=sdot

=sdotsdotsdot

1051040

totuAr

toquAr γτ

38asymp4 mesta

Xi = mestatotiAr

toqiAr 6715

1051540

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 63240

105==

Arto

min


kmdinKvCvTam 50

20000010000000

===

tkmdinUK

KvCvTam 20

2500010000

20000010000000

=sdot=sdot=

kmdinKgodCrTor 830

6000050000

===

tkmdinUK

KgodCrTor 330

2500010000

6000050000

=sdot=sdot=
























15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα





















15020100

=sdot

=sdot

=


3000015000

10015020

100=sdot

sdot=sdot

sdot=


600290100

=sdot

=sdot

=

kmlKmu

VmuPmu 1002903500

10010100=

sdot=

sdot=


3000015000

100600290

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 2

3000015000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα








РЕШЕЊЕ


two= =VsKo

VsKt12

two= h240

402==

sdot h

tui=tu + ti =20+12 = 32 min tui=6032

=053 h


Xu = =sdot

=sdot

=sdotsdotsdot

1522050

totuAr

toquAr γτ

658asymp7 mesta

Xi = mestatotiAr

toqiAr 4953

1521250

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 04350

152==

Arto

min


kmdinKvCvTam 6766

30000020000000

===

tkmdinUK

KvCvTam 3433

3000015000

30000020000000

=sdot=sdot=

kmdinKgodCrTor 1

8000080000

===

tkmdinUK

KgodCrTor 50

3000015000

8000080000

=sdot=sdot=
























10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα





















10030100

=sdot

=sdot

=


3000015000

10010030

100=sdot

sdot=sdot

sdot=


500330100

=sdot

=sdot

=

kmlKmu

VmuPmu 1003303000

10010100=

sdot=

sdot=


3000015000

100500330

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 23

50000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 61

3000015000

50000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα








РЕШЕЊЕ


two= =VsKo

VsKt12

two= h230

302==

sdot h

tui=tu + ti =30+22 = 52 min tui=6052

=087 h


Xu = =sdot

=sdot

=sdotsdotsdot

1723025

totuAr

toquAr γτ

436asymp4 mesta

Xi = mestatotiAr

toqiAr 3193

1722225

asymp=sdot

=sdot

=sdotsdotsdot γτ


Iw= 88625

172==

Arto

min


kmdinKvCvTam 50

40000020000000

===

tkmdinUK

KvCvTam 25

3000015000

40000020000000

=sdot=sdot=

kmdinKgodCrTor 630

8000050000

===

tkmdinUK

KgodCrTor 310

3000015000

8000050000

=sdot=sdot=
























10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα





















10025100

=sdot

=sdot

=


3000030000

10010025

100=sdot

sdot=sdot

sdot=


40040100

=sdot

=sdot

=

kmlKmu

VmuPmu 100402000

1008100=

sdot=

sdot=


3000030000

10040040

100=sdot

sdot=sdot

sdot=

kmdinKgCgNgTg 4

40000200008

=sdot

=sdot

=

tkmdinUK

KgCgNgTg 4

3000030000

40000200008

=sdotsdot

=sdotsdot

=










РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα








РЕШЕЊЕ


two= =VsKo

VsKt12

two= h426

522==

sdot h

tui=tu + ti =10+25 = 35 min tui=6035

=058 h


Xu = =sdot

=sdot

=sdotsdotsdot

2751066

totuAr

toquAr γτ

24asymp2 mesta

Xi = mestatotiAr

toqiAr 6

2752566

=sdot

=sdot

=sdotsdotsdot γτ


Iw= 17466275

==Arto

min


kmdinKvCvTam 3333

60000020000000

===

tkmdinUK

KvCvTam 3333

3000030000

60000020000000

=sdot=sdot=

kmdinKgodCrTor 1

6000060000

===

tkmdinUK

KgodCrTor 1

3000030000

6000060000

=sdot=sdot=





A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

51201522

34217067051

594342

40102122

125115

900

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 40

htihqutu

htitutui

hVsKttw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min1050min301152

67017050

230

302275208306702

4184752

40102122

154115

900

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ

hti

hqutuhtitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20

50min30115283033050

75140

3522752170830751

4184752

40102122

154115

900

3

3

333

3

33

3333

33

3

33

==


=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

72000)353015(900111

42142

42151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10540min43290123

710170540

67130

2522712330710671

68757250

52162

12351269012

800

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 5 50

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20360min62190122

690330360

33230

3522443420690332

5594443

5052162

15811459012

800

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30720min24390124

22150720

75140

3522143170221751

5035143

5052162

15811459012

800

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

76000)353525(80090901

4790

4242151512

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20190min21180141

520330190

330

45228533305203

3443853

40152142

18861738014

600

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 15 40

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20370min42280142

70330370

67130

25227233070671

59147240152142

11711058014

600

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20560min63380143

890330560

25140

2522472330890251

5365472

40152142

18861758014

600

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

57000)252545(60080801

59755880

4768181118

332211

321


asymp===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

170min10980min55890135

151170980

750401522

232330151750

6745232

6062132

712769013

500

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 6 60

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20590min13590133

920330590

67030

1022921033920670

7676921

6062132

611679013

500

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

50min30780min84690134

28150780

72050

1822172170281720

695172

6062132

712769013

500

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

21500)181015(5007209080

28720

2020767

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα


A

B

G S

C




Решење

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrttoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

330min20131min56790155

461330131

330

45226341704613

3383634

60102162

27162739015

1100

1

11

111

1

11

1111

11

1

11


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


tu ti tos




S‐G 10 60

htihqutu

htitutui

hVs

Kttw

htostuitwto

obrttoVsKn

HrZ

vozilaZq

QdnAr

o

o

o

o

330min20450min2790152

780330450

673305522

95450780673

316395460102

162

27162739015

1100

2

22

222

2

22

2222

22

2

22


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ

htihqutu

htitutui

hVsKt

tw

htostuitwto

obrtatoVsKnHr

Z

vozilaZq

QdnAr

o

o

o

o

670min40131min56790155

81670131

4250

60228746708142

3213874

60102162

27162739015

1100

3

33

333

3

33

3333

33

3

33


=+=+=

=sdot

==

=++=++=

asymp=

sdotminus

=

sdotminus

=

asymp=sdotsdot

=sdotsdotsdot

=

γτ

γ


vozilaArAi

vozilaArArArAr

176000)605545(110090901

9090

8181272727

332211

321


===

=++=++=

αααα

Documents

5 ZADACI ORGANIZACIJA...6. У периоду од два месеца или 46 радних дана треба обавити превоз шећерне репе и то 46800 m3