PROBLEM:

The board of directors of General Wheels Co. is considering seven large capital investments. Each investment can be made only once. The 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:

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.

Mutually exclusive alternatives: A group of alternatives where choosing any one alternative excludes choosing any of the others. For instance, when investment opportunities 1 and 2 are mutually exclusive, it means that if you select 1, you cannot select 2 or if you select 2, you cannot select 1.

Furthermore, neither 3 nor 4 can be undertaken unless one of the first two opportunities is under taken.

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 (net present value).

a) Formulate the above problem mathematically (in an algebraic form).

b) Formulate and solve the above problem on a spreadsheet using Excel.

c) Now, suppose that the following restrictions are given in addition to the above problem. Formulate each restriction as a constraint mathematically.

i. You cannot spend more than $60 million on first 3 of the opportunities.

ii. You can select at most 5 investment opportunities to invest.

iii. If you have selected both opportunities 5 and 6 to invest, you have to select either opportunity 1 or 2 to invest.

iv. You have to select at least two of the following opportunities: 1, 3, 5, 7.