The DROF Automobile Company manufactures cars in three pants and then ships them to four regions of the country. The plants can supply the amounts listed in the right column of the following table. The customer demands by region are listed in the bottom row of the table, and the unit cots of shipping an automobile from each pant to each region are listed in the middle of the table. DROF wants to find the lowest cost shipping plan for meeting the demands of the four regions without exceeding the capacities of the plants.
R1 R2 R3 R4 Capacity
P1 131 218 266 120 450
P2 250 116 263 278 600
P3 178 132 122 180 500
Demand 450 200 300 300
a) Write out the Linear Program identify the objective function, decision variables, and constraints.
b) What is the optimal objective function value and optimal decision variables?
c) In your solution you will find that it is optimal to ship zero cars from plant 2 to region 4 because the cost of shipping on this leg, $278 is the high among all legs. What is the highest shipping cost from Plant 2 to Region 4 for which it would be optimal to ship some cars from P2 to R4? Note: only allowed to change the shipping cost from P2 to R4; all other costs and parameters remain exactly the same.