QUESTION 14 7 points Save Aa Three plants P1, P2, and P3 capacities are 4500, 3

Question

QUESTION 14 7 points Save Aa Three plants P1, P2, and P3 capacities are 4500, 3 transportation costs (in S) are provided in the table below of a gas corporation supply gasoline to three of their distributors in the city located at A, B, and C locations. The plants' daily 3000, and 5000, gallons respectively, while the distributors' daily requirements are 5500, 2500, and 4200 gallons. The per-gallon Distributor 0.8 P1 P2 0.7 065 .8 P3 0.5 0.45 07 0.5 Attached is the Sensitivity report for this problem. What is the optimall minimized cost? Microsoft Excel 15.0 Sensitivity Report Variable Cells Cost 0.8 0.5 0.1 0.25 0.00 05 0.1 $8513 P1A SC$13 P18 SDS13 P1C 58514 P2 A SC514 P2 B 1200 0.1 0.35 0.65 E+30 0.35 s0$14 P2 C 5C$15 P3 8 5D515 PSc o s 0.45 0.7 o 0o E+30 0.25 0.00 16+30.00 Constraints 2500 4200 SDS 16 Demand C 4200 SES1S SE$1S P1 Supply 4200 0.2

Explanation / Answer

14. Solving the given LP in solver :

Hence, Optimal Minimized Cost = $ 7750

15. Shadow Price for Distributor B = 0.5

Shadow Price tells us how much the value of the optimal function changes (increases or decreases), when we increase the RHS of the by 1 unit.

Here the RHS changes by = 2600 - 2500 units = 100 units.

16. The reduced costs tell us how much the objective coefficients (unit cost) can be changed before the optimal solution (gallons transported) changes.

the reduced cost for Plant 1 to Distributor B is 0.

HEnce, the optimal solution will not change.

Hence the answer is Not applicable.

Hence, Optimal minimum cost increases by 0.5 when the demand of Distributor B increases by 1 unit.

for 100 units incrrease, the Optimal Cost will increase by = 0.5 * 100 = $ 50

Hence, new minimum cost of transportation, if we increase the Demand of Distributor B to be 2600 units is $ 7800 ($ 7750+$50).

Transportation Costs / gallon ($) Distributor Plant A B C P1 0.8 0.5 1 P2 0.7 0.65 0.8 P3 0.5 0.45 0.7 Distributor Plant A B C total Supply P1 500 2500 1200 4200 <= 4500 P2 0 0 3000 3000 <= 3000 P3 5000 0 0 5000 <= 5000 total 5500 2500 4200 >= >= >= Demand 5500 2500 4200 Optimal Minimized Cost 7750

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