A company is considering seven investments. The cash required for each investment, the net present value (NPV) for each investment, and the ROI, defined as the ratio of NPV to cash required, minus 1, for each investment are as follows:

Each NPV is based on a stream of future revenues, and it includes the cash requirement, which is incurred right away. The budget for investment is $15 million. Partial investment is prohibited, meaning that if the company wants to take part in any of these investments, it must go all the way. It cannot, for example, go halfway in investment 1 by investing $2.5 million and realizing an NPV of $2.8 million. Find the investment policy that maximizes its total NPV. For each case first write the mathematical optimization problem. Then use Excel Solver to solve and find an optimal solution. Solve each part independently of the others. a. Suppose that at most two of investment types 1 through 5 can be selected. b. Suppose that if investment 1 is selected, then investment 3 must also be selected. c. Suppose that at least one of investments 6 and 7 must be selected. d. Suppose that investment 2 can be selected only if both investments 1 and 3 are selected. Each NPV is based on a stream of future revenues, and it includes the cash requirement, which is incurred right away. The budget for investment is $15 million. Partial investment is prohibited, meaning that if the company wants to take part in any of these investments, it must go all the way. It cannot, for example, go halfway in investment 1 by investing $2.5 million and realizing an NPV of $2.8 million. Find the investment policy that maximizes its total NPV. For each case first write the mathematical optimization problem. Then use Excel Solver to solve and find an optimal solution. Solve each part independently of the others. a. Suppose that at most two of investment types 1 through 5 can be selected. b. Suppose that if investment 1 is selected, then investment 3 must also be selected. c. Suppose that at least one of investments 6 and 7 must be selected. d. Suppose that investment 2 can be selected only if both investments 1 and 3 are selected