The board of directors is considering six large capital investment options. Each investment option can be made only once. These options 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:

Investment option Estimated Profit ($millions) Capital Required ($millions)

1 10 25

2 15 30

3 19 50

4 7 15

5 17 40

6 13 30

The total amount of capital available for these investment options is $90 million. Investment options 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 options is undertaken. There are no such restrictions on investment options 5 and 6. The objective is to select the combination of the options that will maximize the total estimated long-run profit (net present value).

a. Formulate an algebraic binary integer programming model and solve it on a spreadsheet for this problem.

b. Perform sensitivity analysis on the amount of capital made available for the investment options (in $millions): 70, 80, 90, 100, 110 and 120. Include both the optimal values of the decision variables and objective function in the output. Interpret your analysis results.