Linear Programming for General Wheels Co: Which investments, maximum profit

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The board of directors of General Wheels Co. is considering seven large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit (net present value) that they will generate as well as in the amount of capital required, as shown by the following table: (See attachment for actual table)

Investment Opportunity Estimated Profit (millions) Capital Required (millions)
1 17 43
2 10 28
3 15 34
4 19 48
5 7 17
6 13 32
7 9 23

The total amount of capital available for these investments is $100 million. Investment opportunities 1 and 2 are mutually exclusive, and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken unless one of the first two opportunities is undertaken. There are no such restrictions on investment opportunities 5, 6 and 7. The objective is to select the combination of capital investments that will maximize the total estimated long-run profit.

a) Formulate and solve a BIP model on a spreadsheet for this problem.

b) Which investments should be undertaken?

c) What will be the maximum profit?

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