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 25 x 1 15 x 2 25 x 3 15 x 4 s t 5 x 1 11 x 2 4 x 3 5 x 4 11 Constraint 1 x 1 x 2 x 3 x 4 2 Constraint 2 x 1 x 2 1 Constraint 3 x 1 x 3 1 Constraint 4 x 2 x 4 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 a What is the net present value of the optimal solution (Round your answer to the nearest whole number ) b How much of the available capital will be spent (Hint Constraint 1 enforces the available capital limit)

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Question: 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

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 25x₁ + 15x₂ + 25x₃+ 15x₄ s.t. 5x₁ + 11x₂ + 4x₃ + 5x₄ 11 {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:

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

b.How much of the available capital will be spent (Hint: Constraint 1 enforces the available capital limit)?

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