Question: Suppose an auto company has three plants in cities A, B and C and two major distribution centers in D, E, F and G. The capacities of the three plants during the next quarter are 100, 200 and 150 cars. The quarterly demands of the four distribution centers are 80, 90, 120 and 160 cars. The transportation costs (which depend on the mileage, transport company etc) between the plants and the distribution centers is as follows:
|
Cost Table
|
Dist Center D
|
Dist Center E
|
Dist Center F
|
Dist Center G
|
|
Plant A
|
4
|
8
|
10
|
9
|
|
Plant B
|
10
|
4
|
15
|
1
|
|
Plant C
|
5
|
12
|
11
|
10
|
Answer the following questions:
(a) Develop a Linear Programming Formulation which includes decision variables, objective function and constraints. State what your decision variables, objective function and constraints stand for.
(b) Solve this problem with Excel-solver add-in. Determine which plant should supply how many cars to which outlet so that the total cost is minimum. Copy and paste the Excel Output to show your work.