Question 4 (30 points) The board of directors of General Wheels Co. is considering eight 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 in the following table (in units of millions of dollars): Investment Opportunity 2 3 4 5 6 7 10 15 19 7 13 9 28 34 48 17 32 23 1 17 43 Estimated Profit Capital Required 8 14 33 The total amount of capital available for these investments is $100 million. Following conditions have to be satisfied as well when making investment decisions: Among investments 1 and 2, you can make at most one of them. 3 . Neither 3 nor 4 can be undertaken if none of the first two investment opportunities is undertaken. Among investments 5, 6, and 7, you have to choose either all of them or none. If investments 2 and 4 are chosen, then among investments 3 and 8 you can choose at most one of them. The objective is to select the combination of capital investments that will maximize the total estimated long-run profit (net present value). Formulate an integer programming model for this problem. Define your decision variables clearly. Question 4 (30 points) The board of directors of General Wheels Co. is considering eight 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 in the following table (in units of millions of dollars): Investment Opportunity 2 3 4 5 6 7 10 15 19 7 13 9 28 34 48 17 32 23 1 17 43 Estimated Profit Capital Required 8 14 33 The total amount of capital available for these investments is $100 million. Following conditions have to be satisfied as well when making investment decisions: Among investments 1 and 2, you can make at most one of them. 3 . Neither 3 nor 4 can be undertaken if none of the first two investment opportunities is undertaken. Among investments 5, 6, and 7, you have to choose either all of them or none. If investments 2 and 4 are chosen, then among investments 3 and 8 you can choose at most one of them. The objective is to select the combination of capital investments that will maximize the total estimated long-run profit (net present value). Formulate an integer programming model for this problem. Define your decision variables clearly