Question 2: A company faces the following capital budgeting decision. Four real estate projects are available for investment. The net present value and expenditures required for each project (in millions of dollars) are as follows: Project 1 2 3 4 5 6 Net Present Value ($ Millions) 10 6 11 14 9 16 Expenditure Required ($ Millions) 70 35 80 60 40 100 The budget for this investment period is $300 million. If either project 1 or 4 is undertaken, they must both be undertaken. At most, two of the projects 2, 3 and 5 can be undertaken. Project 3 has to be undertaken if Project 4 is undertaken. Project 6 cannot be undertaken if Project 4 is undertaken. Formulate an optimization model to find the projects to invest that maximize the total net present value while satisfying all project restrictions and not exceeding the budget. (Do NOT solve the model.) (20 points)
Decision variables
x1 = 1 if Project 1 is undertaken; 0 otherwise.
x2 = 1 if Project 2 is undertaken; 0 otherwise.
x3 = 1 if Project 3 is undertaken; 0 otherwise.
x4 = 1 if Project 4 is undertaken; 0 otherwise.
x5 = 1 if Project 5 is undertaken; 0 otherwise.
x6 = 1 if Project 6 is undertaken; 0 otherwise.
Objective function
Maximize Z = 10 x1 + 6 x2 + 11 x3 + 14 x4 + 9 x5 + 16 x6
Constraints
Budget constraint:
70 x1 + 35 x2 + 80 x3 + 60 x4 + 40 x5 + 100 x6 ≤ 300
Projects 1 and 4 must be undertaken together:
x1 = x4
At most two of projects 2, 3, and 5:
x2 + x3 + x5 ≤ 2
Project 3 must be undertaken if project 4 is undertaken:
x4 ≤ x3
Project 6 cannot be undertaken if project 4 is undertaken:
x4 + x6 ≤ 1
Variable domains
x_i ∈ {0, 1} for i = 1, 2, 3, 4, 5, 6
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