Question #4.

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.

Investment opportunity	Estimated profit ($million)	Capital required ($million)
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 (i.e., they cannot be chosen simultaneously), and so are 3 and 4. Furthermore, 5 can be undertaken only if both 1 and 3 are taken. Opportunity 7 has to be chosen if both 2 and 4 are selected, and Opportunity 7 cannot be invested unless at least one of 5 and 6 is invested. The objective is to select the combination of capital investments that will maximize the total estimated long-run profit (net present value). Formulate this problem as an integer programming model.