10 Q-1 b)i) Land to Wheat = 125 bushels x 0.2 acre per bushel = 25 acre

Wheat Corn Land to Corn = 80 bushels x 0.25 acre per bushel = 20 acreBushels 125 80Revenue/bushel 30 50 ii) Labor purchased = 350 hrs

Constraints Consumed Total Available iii) Max Profit = Rs 4250Sales Cap Wheat 1 0 125 <= 140Sales Cap Corn 0 1 80 <= 120Acre/bushel 0.2 0.25 45 <= 45 Q-1 c)

1.2 2.5 350 <= 350 i) Shadow price of land = Rs 75 and Allowable decrease is 6.666, which is less than 5.So, Max Profit with 40 acre = 4250 - 75*5 = 3875

Objective FunctionCM/bushel 18 25 4250 ii) Allowable Decrease in Bushels of Wheat to affect Product Mix = 6.

Unless Revenue/bushel of wheat decreases below 24, optimal product mix is (125 wheat, 80 corn).So max profit = 125xCM/bushel of wheat + 80 x CM/bushel of corn = 125x(18-4) + 80x25 = 3750

iii) Since Allowable increase = 40 > 10,So, Max Price for 10 labor hrs = Shadow Price x 10 = 2.5 x 10 = Rs 25

iv) Max Price for additional acre = Shadow Price of land = Rs 75.

v) Resources consumed by Soya = 1/4.5 acre per bushel and 8/4.5 lab-hrs.Cost per bushel = 1/4.5 x Shadow price of land + 8/4.5 x Shadow price of lab-hrs= 1/4.5 x 75 + 8/4.5 x 2.5 = 21.11Since CM/bushel > Cost/bushel, Soyabean should be grown.

Labor Costper hour

Labor hrsper bushel

i) Land to Wheat = 125 bushels x 0.2 acre per bushel = 25 acreLand to Corn = 80 bushels x 0.25 acre per bushel = 20 acre

ii) Labor purchased = 350 hrs

iii) Max Profit = Rs 4250

i) Shadow price of land = Rs 75 and Allowable decrease is 6.666, which is less than 5.So, Max Profit with 40 acre = 4250 - 75*5 = 3875

ii) Allowable Decrease in Bushels of Wheat to affect Product Mix = 6.Unless Revenue/bushel of wheat decreases below 24, optimal product mix is (125 wheat, 80 corn).So max profit = 125xCM/bushel of wheat + 80 x CM/bushel of corn = 125x(18-4) + 80x25 = 3750

iii) Since Allowable increase = 40 > 10,So, Max Price for 10 labor hrs = Shadow Price x 10 = 2.5 x 10 = Rs 25

iv) Max Price for additional acre = Shadow Price of land = Rs 75.

v) Resources consumed by Soya = 1/4.5 acre per bushel and 8/4.5 lab-hrs.Cost per bushel = 1/4.5 x Shadow price of land + 8/4.5 x Shadow price of lab-hrs= 1/4.5 x 75 + 8/4.5 x 2.5 = 21.11Since CM/bushel > Cost/bushel, Soyabean should be grown.

Microsoft Excel 15.0 Sensitivity ReportWorksheet: [Assignment.xlsx]Q-1Report Created: 11/29/2015 1:00:16 PM

Variable CellsFinal Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease$B$4 Bushels Wheat 125 0 18 2 6$C$4 Bushels Corn 80 0 25 12.5 2.5

ConstraintsFinal Shadow Constraint Allowable Allowable

Cell Name Value Price R.H. Side Increase Decrease$D$8 Sales Cap Wheat 125 0 140 1E+030 15$D$9 Sales Cap Corn 80 0 120 1E+030 40$D$10 Acre/bushel 45 75 45 1.2 6.6666666667

$D$11 350 2.5 350 40 12Labor hrsper bushel

Price for Each Passenger Demand during One BankDestination Destination

Houston Chicago Miami Phoenix Houston

Origin

Houston 0 197 110 125

Origin

Houston 0Chicago 190 0 282 195 Chicago 130Miami 108 292 0 238 Miami 72Phoenix 110 192 238 0 Phoenix 115

C-H C-M C-P M-H M-C M-P P-H P-C P-M54 98 88 67 105 68 84 90 66

Objective FunctionRev/Passeng 190 282 195 108 292 238 110 192 238

ContraintsC-H demand 1 0 0 0 0 0 0 0 0C-M demand 0 1 0 0 0 0 0 0 0C-P demand 0 0 1 0 0 0 0 0 0M-H demand 0 0 0 1 0 0 0 0 0M-C demand 0 0 0 0 1 0 0 0 0M-P demand 0 0 0 0 0 1 0 0 0P-H demand 0 0 0 0 0 0 1 0 0P-C demand 0 0 0 0 0 0 0 1 0P-M demand 0 0 0 0 0 0 0 0 1H-C demand 0 0 0 0 0 0 0 0 0H-M demand 0 0 0 0 0 0 0 0 0H-P demand 0 0 0 0 0 0 0 0 0C origin cap 1 1 1 0 0 0 0 0 0M origin cap 0 0 0 1 1 1 0 0 0P origin cap 0 0 0 0 0 0 1 1 1H-C cap 0 0 0 0 0 0 0 0 0H-M cap 0 0 0 0 0 0 0 0 0H-P cap 0 0 0 0 0 0 0 0 0

Demand during One BankDestination

Chicago Miami Phoenix123 80 110

0 98 88105 0 68

90 66 0

H-C H-M H-P123 80 110

197 110 125 198145

Consumed Availibility0 0 0 54 <= 1300 0 0 98 <= 980 0 0 88 <= 880 0 0 67 <= 720 0 0 105 <= 1050 0 0 68 <= 680 0 0 84 <= 1150 0 0 90 <= 900 0 0 66 <= 661 0 0 123 <= 1230 1 0 80 <= 800 0 1 110 <= 1100 0 0 240 <= 2400 0 0 240 <= 2400 0 0 240 <= 2401 0 0 123 <= 2400 1 0 80 <= 2400 0 1 110 <= 240

Microsoft Excel 15.0 Sensitivity ReportWorksheet: [Assignment.xlsx]Q-4Report Created: 11/29/2015 3:45:01 PM

Variable CellsFinal Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease$B$13 C-H 54 0 190 5 190$C$13 C-M 98 0 282 1E+030 92$D$13 C-P 88 0 195 1E+030 5$E$13 M-H 67 0 108 130 108$F$13 M-C 105 0 292 1E+030 184$G$13 M-P 68 0 238 1E+030 130$H$13 P-H 84 0 110 82 110$I$13 P-C 90 0 192 1E+030 82$J$13 P-M 66 0 238 1E+030 128$K$13 H-C 123 0 197 1E+030 197$L$13 H-M 80 0 110 1E+030 110$M$13 H-P 110 0 125 1E+030 125

ConstraintsFinal Shadow Constraint Allowable Allowable

Cell Name Value Price R.H. Side Increase Decrease$N$19 C-H demand Consumed 54 0 130 1E+030 76$N$20 C-M demand Consumed 98 92 98 54 76$N$21 C-P demand Consumed 88 5 88 54 76$N$22 M-H demand Consumed 67 0 72 1E+030 5$N$23 M-C demand Consumed 105 184 105 67 5$N$24 M-P demand Consumed 68 130 68 67 5$N$25 P-H demand Consumed 84 0 115 1E+030 31$N$26 P-C demand Consumed 90 82 90 84 31$N$27 P-M demand Consumed 66 128 66 84 31$N$28 H-C demand Consumed 123 197 123 1E+030 123$N$29 H-M demand Consumed 80 110 80 1E+030 80$N$30 H-P demand Consumed 110 125 110 1E+030 110$N$31 C origin cap Consumed 240 190 240 76 54$N$32 M origin cap Consumed 240 108 240 5 67$N$33 P origin cap Consumed 240 110 240 31 84

Factory to Depot Costs Depot to Customer CostsLiverpool Brighton C1 C2 C3

Liverpool 0 Liverpool 1 1.5Brighton 0 Brighton 2Newcastle 0.5 Newcastle 1.5 0.5Birmingham 0.5 0.3 Birmingha 1 0.5 0.5London 1 0.5 London 1.5 2Exeter 0.2 0.2 Exeter 0.2

Liverpool outputC1 C2 C3 C4 C5 C6

Liverpool 50000 0 0 0BrightonNewcastle 0 0 0 20000Birmingham 0 0 0 0 0London 0 0 55000 0Exeter 0 20000 5000 0

Brighton outputC1 C2 C3 C4 C5 C6

LiverpoolBrighton 0Newcastle 10000 40000 0 0Birmingham 0 0 0 0 0London 0 0 0 0Exeter 0 15000 0 0

Cost (Liverpool output 50000 0 0 4000 56000 10000Cost (Brighton output) 0 5000 20000 3000 0 0Total Cost 50000 5000 20000 7000 56000 10000 148000

ConstraintsLiverpool cap 50000 0 0 20000 60000 20000 150000Brighton cap 0 10000 40000 15000 0 0 65000Newcastle cap 0 10000 40000 0 0 20000 70000Birmingham cap 0 0 0 0 0 0 0London cap 0 0 0 0 55000 0 55000Exeter cap 0 0 0 35000 5000 0 40000C1 demand 1 0 0 0 0 0 50000C2 demand 0 1 0 0 0 0 10000C3 demand 0 0 1 0 0 0 40000C4 demand 0 0 0 1 0 0 35000

C5 demand 0 0 0 0 1 0 60000C6 demand 0 0 0 0 0 1 20000

Depot to Customer CostsC4 C5 C6

2 1

1.5 11 0.5

0.5 1.51.5 0.5 1.5

<= 150000<= 200000<= 70000<= 50000<= 100000<= 40000>= 50000>= 10000>= 40000>= 35000

>= 60000>= 20000