please do not solve with excel, but with long written answers. thank you.

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 (Smillion) $17 Capital required (Smillion) 1 $43 2 $10 $28 3 $15 S34 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