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 Max 20 x 1 30 x 2 10 x 3 15 x 4 s t 5 x 1 7 x 2 12 x 3 11 x 4 21 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 selected 0, otherwise Solve this problem to optimality and answer the following questions A) Which of the warehouse locations will will not be selected Location 1, Location 2, Location 3, Location 4 B) What is the net present value of the optimal solution C) 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 firm's goal is to maximize

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. Max 20x₁ + 30 x₂ + 10x₃ + 15x₄ s.t.5x₁ + 7x₂ + 12x₃ + 11x₄ 21 {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,iflocationjisselected0,otherwise

Solve this problem to optimality and answer the following questions:

A) Which of the warehouse locations will/will not be selected?

Location 1, Location 2, Location 3, Location 4?

B) What is the net present value of the optimal solution?

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

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