A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital.

Let x_j = 1 if location x_j is selected; 0 if not (j = 1, 2, 3, 4)

Maximize NPV = 30x₁ + 20x₂ + 10x₃ + 15x₄

subject to the following constraints:

(Constraint 1) 5x₁ + 12x₂ + 7x₃ + 11x₄ 21

(Constraint 2) x₁ + x₂ + x₃ + x₄ 2

(Constraint 3) x₁ + x₃ 1

(Constraint 4) x₁ + x₂ 1

(Constraint 5) x₁ = x₄

a) Which of the constraints enforces a contingent relationship?

b) Which of the constraints enforces that at most one of the two locations must be chosen?

c) Set up the programming model in Excel and run the Solver to find the optimal solution. Which locations are Selected? Selections: ["Location 1", "Location 2", "Location 3", "Locations 1 and 3", "Locations 1 and 4", "NIC"]

d) What is the expected NPV of the optimal solution?