Weekwise Course Plan Rev Sept 15 Homework

8/17/2019 Weekwise Course Plan Rev Sept 15 Homework

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Course StandardizationManagement Science

Course Code: MGT 691

RevisedSeptember 2015



Management Science MGMT 691

Tet !oo": #n $ntroduction to Management Science% 1&t' (dition b) *avid

R+ #nderson% *ennis ,+ S-eene) T'omas # .i//iams% ,ere) *Camm ipp Martin, South-Western CengageLearning.{Soft copy is available at elibrary\gabbas\MS

Software: - !M-"M #er $- Manage%ent Scientist- MS &'cel

!n Line "ui((es: - )irst *ui( + after three sessions- Secon *ui( + after ve sessions- hir *ui( + after nine session

Midterm (am: $t -i// not be sot-are based eam and -i// be conducted inregu/ar c/assrooms+

3ina/ (am: $t -i// be sot-are based eam and -i// be conducted in /ab+

Sept+% 2015 1




.ee" 4 1

01+1 $ntroduction

Give a brie introduction o t'e subect

01+2+ Revie- o !asic Mat'

01+2+1 Grap' o a /inear euation 4 do-n-ard s/oping and up-ard s/oping/ines% 'orizonta/ and vertica/ /ines and /ine passing t'roug' origin+

01+2+2 Concept o 7% ≤ and ≥ region

01+2+& 8oint o intersection

01+& inear 8rogramming

01+&+1 $ntroduction C'apter 2;

01+&+2 *iscuss a maimization eamp/e an eamp/e given at section 2+1 isadvised;+

01+&+& *iscuss t-o basic assumptions o 8:

i+ #// re/ations'ips are /inear

ii+ <on=negativit) constraint

01+&+> 8rob/em s'ou/d be so/ved manua//) b) Grap'ic Met'od+

01+&+5 3or optima/ so/ution use Corner 8oint Met'od+ $soproit ine So/utionMet'od is not advisab/e+ ?o-ever% it is an option or t'e acu/t)+

01+> *iscuss t'e concept o uti/ization and un=uti/ization s/ac"; o a resource+

01+5 (ercise: #// t'e uestions and case studies given at t'e end o c'apter 2

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.ee" 4 2

02+1+ *iscuss a minimization eamp/e+ 3o//o-ing eamp/e is advised:

<utrients

Contents per unitMinimum

Reuirements3ood 4 $ 3ood 4 $$

Ca/cium 10 > 20

8rotein 5 5 20

@itamin 2 6 12

8rice Rs+6A7 Rs+10A7 =

02+2+ $t s'ou/d be so/ved as per t'e met'ods discussed in irst -ee"+

02+&+ *iscuss t'e concept o ac'ievement o t'e target and surp/us+

02+> $ntroduce sot-are 8BM=M or .indo-s+

02+5+ *iscuss e- more eamp/es+ 3o//o-ing eamp/es are advised:

02+5+1 #n eamp/e -it' D7E constraint

# 'omeo-ner -ants to paints 'er 'ouse+ T'e paint must possess aviscosit) o at /east 200 centipoises+ 3or t'e desired /eve/ o bri//ianceand durabi/it)% t'ere must be at /east 1> grams o a c'emica/=# and &0

grams o c'emica/=! in eac' ga//on o paint+T'ere are t-o "inds o paint $ and $$; avai/ab/e to 'er+ T)pe $ cost F6and $$ cost F> per ga//on+ 8er ga//on speciications o paints are aso//o-s:

8aint=$ 8aint=$$

@iscosit) >00 100C'emica/=# 20 10C'emica/=! 20 60

T'e 'omeo-ner decides to b/end $ and $$ in order to meet t'e t'reereuirements at a minimum cost+ ?o- muc' o $ and $$ s'ou/d be usedin eac' ga//on o t'e b/end in order to minimize cost+

{Solution: Paint I = 0.4 gallons, Paint II = 0.6 gallon and Cost = $ 4.80}

Sept+% 2015 &




02+5+2 #n eamp/e -it' mu/tip/e easib/e regions

# business irm is p/anning to advertise a specia/ anniversar) sa/e on

radio and T@ during a particu/ar -ee"+ 3or t'at% a maimum budget oF16%000 is approved+ $t is ound t'at radio commercia/ cost F00 perspot -it' a minimum contract o ive spots+ T@ commercia/ costF>%000 per spot+ !ecause o 'eav) demand% on/) our T@ spots areavai/ab/e in t'e designated -ee"+ # stud) revea/s t'at a T@ spot is sitimes eective as a radio spot in reac'ing potentia/ customers+ ?o-s'ou/d t'e irm a//ocate its advertising to attract t'e /argest possib/enumber o potentia/ customersH

{Solution: On Radio zero sots and on !" #our sots and PC = 4 units}

02+6+ Reso/ve studentsI uarries+

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.ee" 4 &0&+1 3urt'er eamp/e:

# compan) 'as t-o grades o inspectors $ and $$% -'o are to be assigned ora ua/it) contro/ inspection+ $t is reuired t'at at /east 1%00 pieces be

inspected per da) 'ours;+ Grade=$ inspector can c'ec" 25 pieces per 'our-it' an accurac) o 9J+ Grade=$$ can c'ec" 15 pieces per 'our -it' anaccurac) o 95J+

T'e 'our/) -age rate o Grade=$ and $$ is F> and F& respective/)+ (ac' timean error is made% t'e cost to t'e compan) is F2+ T'e compan) 'as avai/ab/eor t'e inspection ob eig't grade=$ and ten grade=$$ inspectors+ T'e compan)-ants to determine optima/ number o inspectors to be appointed or t'e ob-it' obective to minimize tota/ cost+

{ Solution: %u&'er o# (rade I Inse)tors = 8 and (rade II inse)tors =

*.6+ and &ini&u& )ost = Rs.80}

0&+2 *iscuss t'ird basic assumption o inear 8rogramming 4 #// variab/es arecontinuous+

0&+& @arious Situations:

0&+&+1 $ninite so/ution+

0&+&+2 3easib/e region is on/) a D8ointE

0&+&+& ines do not intersect+

0&+&+> <o easib/e region+

0&+&+5 *iscuss e- situations or positive s/ope+

i+ # urniture manuacturer is producing a dining tab/es and c'airs+ #set consist o 5 c'airs and a tab/e+ *eve/op a constraint+

C K 7 5Tii+ # urniture manuacturer is producing a dining tab/es and c'airs+ #

set consist o 5 c'airs and a tab/e+ ?istorica/ data revea/s t'atdemand or etra c'airs is 15 per cent+ *eve/op a constraint+

C K 7 5T L 0+155T;

Sept+% 2015 5




iii+ # button manuacturer 'as one mac'ine -'ic' can produce 65 buttons o t)pe # or >5 buttons o t)pe ! in one minutes+ Compan)'as t-o 'ours+ *eve/op a constraint+

A65 L NA>5 O7 120

iv+ #nd e- more eamp/es+

0&+&+> # compan) produces t-o t)pes o s'irts% 'a/ s/eeves and u// s/eeves+$ a// resources are diverted to -ard 'a/ s/eeves s'irt% compan) can

produce 1200 s'irts+ $t is urt'er given t'at time reuired to produceu// s/eeves s'irt is t-ice o time reuired or 'a/ s/eeves s'irts+*eve/op a constraint+

#ssumption: Time reuired or a 'a/ s/eeves s'irt is one 'our+

$ts conseuences: i+ .e 'ave 1200 'ours+ ii+ Time reuired or a u// s/eeves s'irt is t-o 'ours+

L 2N O7 1200

0&+> Reso/ve studentsI uarries on eercise o c'apter t-o+ 0&+5+ # uiz is advised+

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.ee" 4 >

0>+1+ Sensitivit) 8ost Bptima/ #na/)sis C'apter 4 &;

0>+1+1 *iscuss on/) maimization prob/em -it' resource constraints P t)pe

constraints;+

0>+1+2 Sensitivit) s'ou/d inc/ude o//o-ing:

i+ Rig't ?and Side Sensitivit) #na/)sis+ii+ *eve/opment o 8riorit) ist concept o unit -ort';+iii+ C'anges in coeicients o obective unction+

0>+1+& To deve/op t'e concepts% a sma// prob/em ma) be so/ved manua//)%'o-ever% u/timate/) it s'ou/d be so/ved t'roug' M+

0>+2 Give eamp/es -it' more t'an t-o variab/es+

0>+&+ Reso/ve studentsI uarries+

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.ee" 4 5

05+1+ inear 8rogramming #pp/ications -it' more t'an t-o variab/es C'apter >;

*iscuss o//o-ing eamp/es:

i+ Media Se/ection >+1;ii+ Mar"eting Researc' >+1;iii+ 8orto/io Se/ection >+2;iv+ 3inancia/ 8/anning >+2;v+ C'0>+pptvi+ ?andout 8 e/ib+:gabbasMS;

05+2 Reso/ve studentsI uarries+

05+&+ # uiz is advised+ 05+>+ T'is comp/etes t'e course or Mid=Term (amination+

%ote: It -ill not 'e so#t-are 'ased ea& and -ill 'e )ondu)ted in regular

)lassroo&s.

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.ee" 4 6

06+1+ Transportation Mode/s C'apter 4 6;

*iscuss t'e concept o transportation prob/em

06+2+ *iscuss eamp/e given at section 6+1 and so/ve it t'roug' transportationmodu/e o M+

06+&+ 8rob/em @ariation = nba/anced Mode/s

06+&+1 *iscuss t'e concept o unba/anced mode/+

06+&+2 3o//o-ing eamp/es are advised:

i+*emand O Supp/)

8rob/em:

/ - 0 / - 1 / - 2 / - $ / - 3 Supply

S - 0 $0 21 12 1$ 20 3,134

S - 1 15 03 2$ 06 13 7,544

S - 2 $0 $4 $2 25 15 02,$44/e%a

n 0,444 0,14404,23

4 $,344 7,6441$,634\18,$34

So/ution:

!pti%alcost 9

851534/ -0 / - 1 / - 2 / - $ / - 3 /u%%y

S - 0 3,134

S - 1

0,44

4 0,144 0,044 $,344S - 2 $,444 7,644 0,344

*iscuss t'e concept o dumm) destination

Sept+% 2015 9




ii+ *emand K Supp/)

8rob/em

/ - 0 / - 1 / - 2 / - $ / - 3 Supply

S + 0 80 $7 08 80 12 83.655

S + 1 $$ 1$ 2$ 80 27 006.213

S + 2 15 05 83 00 $$ 0$.283/e%an

16.88

811.65

7043.$8

384.22

107.28

3123.503\066.875

So/ution:

!pti%al cost9 3833.07

/ - 0 / - 1 / - 2 / - $ / - 3

S - 083.6

64

S - 116.8

7411.6

6426.$

546.52

407.2

74

S - 2

0$.2

74

/u%%y28.0

$4

*iscuss t'e concept o dumm) source+

7777777 (nd o t'e session 7777777

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.ee" 4 Q

0Q+1+ 8rob/em @ariation or Restrictions

0Q+1+1 *iscuss t'e o//o-ing situations:

i+ Maimization obective+ii+ Route capacities or route minimums+iii+ nacceptab/e routes+

0Q+1+2 !ecause o t'e restrictions% transportation modu/e o M -i// not -or"and -e need to transorm a transportation prob/em to a /inear

programming mode/+

0Q+2+ Transormation o Transportation Mode/ to inear Mode/+

0Q+2+1 *iscuss t'e transormation o t'e transportation mode/s to a /inearmode/ and so/ving it t'roug' /inear programing modu/e o M+

0Q+2+2 (amp/e given at section 6+1 is advised+

0Q+2+& So/ve it t'roug' /inear programming modu/e o M+

0Q+2+> Students s'ou/d be encouraged to enter data in (ce/ and t'en

cop)Apaste it to M+

0Q+2+5 Butput o 8 modu/e s'ou/d be presented as per t'e ormats given be/o-:

Route nitsS'ipped

Cost per nit

Tota/ Cost3rom To

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

Sept+% 2015 11




0Q+&+ #not'er eamp/e+

0Q+&+1 8rob/em:

Custo%er

- 0Custo%er

- 1Custo%er

- 2Custo%er

- $ Supplylant - 00 04 13 $3 01,344lant - 21 12 03 25 05,054lant - 18 0$ 14 2$ $,234/e%a 1,744 11,344 5,644 $,654 26,454\23,

$t is urt'er given t'at

= 100 per cent demand o Customer42 s'ou/d be met as 'e is a priorit)customer+

= Supp/) rom 8/ant41to Customer=& s'ou/d not be more t'an 50J oits production+

0Q+&+2 So/ution

1 2 3 4

Custo%er

- 0Custo%er

- 1Custo%er

- 2Custo%er

- $ Supply

1 lant - 00 04 13 $3 01,3442 lant - 21 12 03 25 05,0543 lant - 18 0$ 14 2$ $,234 4 /u%% 4 4 4 4 $,434

/e%a 1,744 11,344 5,644 $,654

0Q+&+2+1 Mode/: Min+: C 7 1111 L 1012 L 251& L >51> L &221 L 2&22 L 152& L &2> L 26&1 L 1>&2 L 20&& L&>&>

s+t+ 11 L 12 L 1& L 1> O7 12500 ========== 121 L 22 L 2& L 2> O7 110 ========== 2&1 L &2 L && L &> O7 >&50 ========== &>1 L >2 L >& L >> O7 >050 ========== >11 L 21 L &1 L >1 K7 2Q00 ========== 512 L 22 L &2 L >2 K7 22500 ========== 61& L 2& L && L >& K7 900 ========== Q1> L 2> L &> L >> K7 >90 ==========

Sept+% 2015 12




>2 7 0 ========== 91& O7 6250 ========== 10

0Q+&+2+2 Resu/ts

Route nitsS'ipped

Cost per unit

Tota/ Cost

3rom To8/ant 1 Customer = 1 0 11 0

8/ant 1 Customer = 2 6250 10 62500

8/ant 1 Customer = & 6250 25 156250

8/ant 1 Customer = > 0 >5 0

8/ant 2 Customer = 1 0 &2 0

8/ant 2 Customer = 2 10550 2& 2>2650

8/ant 2 Customer = & 2650 15 &9Q50

8/ant 2 Customer = > >90 & 192>0

8/ant & Customer = 1 0 26 0

8/ant & Customer = 2 >&50 1> 609008/ant & Customer = & 0 20 0

8/ant & Customer = > 0 &> 0

&5%0&0 Q51%290

0Q+>+ *erive a genera/ /inear programming mode/ as given on page 262+

Given:

C;S!M&<S

S;L

=> >> >>> ? @

) A C . ! < > & S

> B00C00

B01C01

B02C02

? B0nC0n

S0

>> B10C10

B11C11

B12C12

? B1nC1n

S1

>>> B20C20

B21C21

B22C22

? B2nC2n

S2

? ? ? ? ? ?

MB%0

C%0 B%1 C%1 B%2 C%2 ? B%n C%n S%

/&MA@/ /0 /1 /2 ? /n

Sept+% 2015 1&




*erivation

Supply ¿ Fac I : X 11+ X 12+…+ X 1 n ≤ S1∑ j=1

n

X 1 j ≤ S1

Supply ¿ Fac II : X 21+ X 22+…+ X 2 n ≤ S 2∑ j=1

n

X 2 j ≤ S 2

.

.

.

Supply ¿ Fac M : Xm

1+ Xm

2+…+ Xmn≤Sm∑ j=1

n

Xmj≤Sm

Supp/) Constraints

∑ j=1

n

Xij ≤Si

.'ere i 7 1%2%&%U%m

Received by Cus I : X 11+ X 21+…+ Xm 1 ≥ D 1∑ I =1

m

Xi 1 ≥ D 1

Received by Cus II : X 12+ X 22+…+ Xm2≥ D2∑i=1

m

Xi 2≥ D 2

.

.

.

Received by Cus N : X 1 n+ X 2 n+…+ Xmn ≥ Dn∑i=1

m

Xim≥ Dm

*emand Constraints

∑i=1

m

Xij ≥ Dj

.'ere 7 1%2%&%U%n

Bbective unction: Min+: C 7 c1111 L c1212 L D cmnmn

Min. : C =∑i=1

m

∑ j=1

n

cijXij

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.ee" 4

0+1+ Transs'ipment Mode/s section 6+&;

*iscuss t'e concept o transs'ipment+

0+2 Transs'ipment modu/e is not avai/ab/e in M% t'ereore% transs'ipment prob/em -i// be so/ved t'roug' /inear programming mode/+

0+& *iscuss t'e eamp/e given at section 6+&

0+> 8rob/em variations as discussed in transportation prob/em ma) a/so bediscussed 'ere+

0+5+ Butput o 8 modu/e s'ou/d be presented as per t'e ormats given be/o-:

Routenits

S'ippedCost per

nitTota/ Cost

3rom Tointermediate

;.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

Sub = Tota/

Routenits

S'ippedCost per nit Tota/ Cost

3romintermediat

e

To3ina/;

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

Sub 4 Tota/

Tota/ Cost o Transs'ipment

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.ee" 4 9

09+1+ #ssignment Mode/s Section 6+2;

*iscuss t'e concept o #ssignment mode/+

09+2 So/ve t'e eamp/e given at section 6+2 t'roug' assignment modu/e o M+

09+& *iscuss ba/ance as -e// as unba/ance mode/s+

09+> # uiz is advised+

09+5 Reso/ve studentsI uarries+

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.ee" 4 10

10+1+ Revie- o Matri a/gebra

10+1+1 *iscuss matri mu/tip/ication

10+1+2 *iscuss matri mu/tip/ication on (ce/+

10+1+& So/ve o//o-ing eamp/e on (ce/:

Given: A0= 10 20 18 and T =[0.2 0.3 0.5

0.9 0.1 0.0

0.7 0.2 0.1]

3ind #1 .'ere #1 7 #0T

#2 .'ere #2 7 #1T+++

#50 .'ere #50 7 #>9T

10+1+> So/ution: A1=[ 32.60 8.60 6.80 ] A 2=[ 19.02 12.00 16.98 ]

+++

A50= 23.85 10.90 13.25

10+2+ Mar"ov #na/)sis C'apter 16;

10+2+1 *iscuss basic concept o Mar"ov ana/)sis+

10+2+2 *iscuss t'e basic assumptions o Mar"ov ana/)sis

10+&+ Stead) State 8robabi/ities

10+&+1 *iscuss t'e concept o stead state probabi/ities

10+&+2 *iscuss t'e eamp/e given at section 16+1+

10+>+ # uiz is advised+7777777 (nd o t'e session 7777777

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.ee" 4 11

11+1+ So/ve Mar"ov prob/ems t'roug' (ce/+

11+2+ So/ve Mar"ov prob/em t'roug' M+

11+&+ *iscuss t'e ca/cu/ations o stead) state probabi/ities manua//) on/) t-ostates; 4 See page Q6 and Q69+

(amp/e:

[ p 1 p 2 ][0.92 0.08

0.12 0.88]= [ p 1 p 2 ] we!e p 1∧ p 2 a!e s"eady s"a"e p!#b .

0+92p1 L 0+12p2 7 p1 ================== 1

0+0p1 L 0+p2 7 p2 ================== 2 p1 L p2 7 1 ================== &

So/ve e 4 1 and & simu/taneous/) or e 4 2 and &;Resu/t: p1 7 0+6 and p2 7 0+>@eri) t'e ans-er t'roug' M

<ote: e 4 1 and e 4 2 are t'e same euations% t'ereore% -e need e 4 & toso/ve t'e s)stem+

11+>+ Stead) state probabi/ities -it' more t-o states s'ou/d be so/ved t'roug'M+

11+5+ #n app/ication = o//o-ing eamp/e is advised:

11+5+1 8rob/em:

.e 'ave t'ree super stores in a region 8opu/ar Store% Mart n Mart and(ce//ent Mart+ # mar"et researc' sponsored b) (ce//ent Mart; -as

conducted to stud) t'e brand s-itc'ing be'avior o t'e consumers+Consu/tant gave t'e distribution o customers and a transition matri-'ic' is as o//o-s:

E of opul Mart n &'celle

Sept+% 2015 1




Custo%ers

arStore Mart

nt

opularStore

3,3444.6$ 4.42 4.42

Mart n

Mart

7,544

4.43 4.62 4.41&'cellent 10,144 4.00 4.45 4.50

T'e Genera/ Manger% mar"eting o (ce//ent Mart 'ave rea/ized t'eissue and p/anned a ne- mar"eting strateg)+ ?e estimate a ne-transition matri -'ic' is as o//o-s:

opularStore Mart n Mart

&'cellent

opular

Store 4.60 4.42 4.48Mart nMart 4.43 4.64 4.43&'cellent 4.4$ 4.48 4.64

T'e cost o ne- strateg) is Rs+6&A7 mi//ion per mont' and epectedrevenue per mont' is Rs+%000A7+

S'ou/d -e emp/o) ne- strateg)H Support )our ans-er+

11+5+2 So/ution:

Resu/ts -it' t'e initia/ transition matri:

opularStore

Mart nMart

&'cellent

(nding number given initia/; 1Q%9>0 12%>20 >%1>0

Stead) State probabi/it) 0+52 0+&6 0+12

Resu/ts -it' t'e ne- transition matri:

opular

Store

Mart n

Mart

&'cellen

t(nding number given initia/; 11>>5 10Q92 1226&

Stead) State probabi/it) 0+&& 0+&1 0+&6

(stimated increase in number o customers due to ne- strateg) -ou/d be 5,012 F01,182 + $,0$4G.

Sept+% 2015 19




Aitional <evenue 9 5,012 ' <s.5,444 9<s.8$,65$,444

Cost o <e- Strateg) 7 Rs+6&%000%000A7 <et !eneit 7 Rs+1%9>%000A7

Nes% -e s'ou/d go or ne- strateg)+

11+6+ (ercise: 8rob/em number 1 4 9 given at t'e end o c'apter 167777777 (nd o t'e session 7777777

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.ee" 4 12

12+1+ Reso/ve studentsI uarries+

12+2+ *iscuss t'e concept o absorbing state probabi/ities+

12+&+ *iscuss t'e eamp/e 16+2 #ccount Receivab/e #na/)sis+ T'is s'ou/d beso/ved on M+ Manua/ so/ution is an option or t'e acu/t)+

12+>+ (ercise: 8rob/em number 10 4 1> and case prob/em given at t'e end oc'apter 16+

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.ee" 4 1&

1&+1+ 8roect Sc'edu/ing 8(RTAC8M; 4 C'apter 9

*iscuss t'e basic concept o proect sc'edu/ing+

1&+2+ *iscuss t'e eamp/e given at 9+1

(amp/e must be so/ved on M

1&+&+ Reso/ve studentsI uarries+

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.ee" 4 1>

1>+1 *iscuss t'e eamp/e given at 9+2+ $t s'ou/d be so/ved on M

1>+2 Statistica/ inerence on proect sc'edu/ing t'roug' M+

3o//o-ing eamp/e is advised:

#n average comp/etion time o a proect% based on 8(RT mode/% is estimatedat &6+2 mont's -it' t'e standard deviation o 2+5 mont's+

i+ *etermine t'e probabi/it) o comp/eting t'e proect -it'in >0 mont's+

{Solution: 8/.* }

ii+ *etermine t'e time b) -'ic' t'e management can be 95 per centconident o comp/eting t'e proectH

{Solution: 4*.06 &ont1s}

iii+ .'at is t'e c'ance t'at proect -i// ta"e at /east &5 mont'sH

{Solution: +2./6}

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.ee" 4 15

15+1 *iscuss proect sc'edu/ing -it' time 4 t'e concept o cras'ing activities+T'is must be so/ved on M

15+2 *iscuss t'e concept o determining /east increase in cost over t'e norma/cost in order to comp/ete t'e proect in t'e cras' time+

15+& *iscuss t'e concept o time and budget+

15+> #n eamp/e

#ctivit)

#ctivit) time

Cras'time

<orma/Cost

Cras'Cost

8redecessor 1

8redecessor 2

# 1 1> 15000 19000

! 2 1 1000 22500

C & 2 2500 &200 !

* 5 > >500 5Q00 !

( Q 5 6000 Q500 C

3 > > &500 &500 * (

G 15 12 1200 16100 # 3

15+5 Bvera// revie- o t'e course+

7777777 (nd o t'e session 7777777

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Documents

Weekwise Course Plan Rev Sept 15 Homework