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:

  1. Which of the warehouse locations will/will not be selected?
    Location 1 will
    Location 2 will
    Location 3 will
    Location 4 will

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