1. A management is considering investing in several projects that have varying capital requirements over the next four years. Faced with limited budget each year, the management must decide which projects to undertake. The goal is to maximize the total net present value of the portfolio of projects. The estimated net present value for each project, the capital requirements, and the available budget over the four-year are shown in the table below. Project 1 Project 2 Project 3 Project 4 Project 5 Budget (5) Net present value ($) 9,000 4,000 5,000 3,000 7,000 Year 1 2,000 1,000 2,300 800 4,500 8,000 Year 2 1,500 500 2,000 1,000 2,500 6,000 Capital Requirements ($) Year 3 4,000 2,000 1,500 600 1,000 7,000 Year 4 6,000 1,700 900 1,500 2,000 9,500 a. (10 pts.) Formulate the problem into an ILP model. b. (10 pts. Use Excel Solver to find an optimal solution and provide the answer report. What are the optimal solution and the optimal objective function value? Optimal solution: Optimal objective function value: c. Formulate each of the following constraints. (5 pts.) Project 1 or 3 must be undertaken, but not both. (5 pts.) Projects 2 cannot be undertaken unless projects 1 and 3 also are undertaken