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# Linear Programming for General Wheels Co.

See attached file.

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?

#### Solution Summary

The solution discusses linear programming for the General Wheels Co. including investments and maximum profit.

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