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 a Unit of Product

Machine A B C

1 $13 $ 9 $10

2 $11 $12 $ 8

The time required to produce each product on each machine is summarized below:

Time (Hours) Needed to

Produced a Unit of Product

Machine A B C

1 0.4 1.1 0.9

2 0.5 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.

Setup Costs for Producing

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?