A company manufactures three products: A, B, and C. The company currently has an order for three units of product A, 7 units of product B, and 4 units of product C. There is no inventory for any of these products. All three products require special processing that can be done on one of two machines. The cost of producing each product on each machine is summarized below:
| Cost of producing the unit |
a |
b |
c |
| Machine |
|
|
| 1 |
13 |
9 |
10 |
| 2 |
11 |
12 |
8 |
The time required to produce each product on each machine is summarized below:
| Machine hours needed |
|
|
|
| Machine |
a |
b |
C |
| 1 |
.4 |
1.1 |
.9 |
| 2 |
.5 |
1.2 |
1.3 |
Assume that machine 1 can be used for eight hours and machine 2 can be used for six hours. Each machine must undergo a special setup operation to prepare it to produce each product. After completing this setup for a product, any number of that product type can be produced. The setup costs for producing each product on each machine are summarized below.
| Set up Costs |
|
|
|
| Machine |
a |
b |
c |
| 1 |
55 |
93 |
60 |
| 2 |
65 |
58 |
75 |
a. Formulate an ILP model to determine how many units of each product to produce on each machine to meet demand at a minimum cost.
b. Implement your model in a spreadsheet and solve it.
c. What is the optimal solution?