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

Max 35x₁ + 25x₂ + 15x₃+ 30x₄ s.t. 7x₁ + 8x₂ + 7x₃ + 13x₄ 18 {Constraint 1} x₁ + x₂ + x₃ + x₄ 2 {Constraint 2} x₁ + x₂ 1 {Constraint 3} x₁ + x₃ 1 {Constraint 4} x₂ = x₄ {Constraint 5}

xj = {1, if location j is selected0, otherwisexj = 1, if location j is selected0, otherwise

Solve this problem to optimality and answer the following questions:

1. Which of the warehouse locations will/will not be selected?

location 1 will
location 2 will
location 3 will
location 4 will

2. What is the net present value of the optimal solution? (Round your answer to the nearest whole number.)

3. How much of the available capital will be spent (Hint: Constraint 1 enforces the available capital limit)? (Round your answer to the nearest whole number.)