Question: 4. Six projects are being considered for execution over the next 3 years. The expected returns in net present value and yearly cash expenditures of

4. Six projects are being considered for execution over the next 3 years. The expected returns in net present value and yearly cash expenditures of each project as well as funds available per year (all units are million dollars) are as follows (Figure 3): Annual Expenditures Project Year 1 Year 2 Year 3 Returns 8 2 3 1 5 9 4 7 2 7 6 3 4 2 9 25 20 10 15 21 12 28 6 Available Funds 8 26 22 Figure 3 There are some extra (logical) constraints due to relations between projects: - (Logical 1) There can be at most four projects selected. - (Logical 2) Project 5 depends on project 2 (i.e., if project 5 selected, then project 2 must also be selected) - (Logical 3) Either project 5 or project 6 should be selected - (Logical 4) If project 2 is selected, then project 3 cannot be selected. Formulate an Integer Programming (IP) model to determine which projects should be selected for execution over the next 3 years to maximize the total returns of the executed projects for available funds in each year? (Note: use binary (0-1) decision variable x; in your formulation to denote whether we decide to select any project j or not.)

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