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A firm has prepared the following binary integer program to evaluate a number of potential locations...

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Advance Math

A firm has prepared the following binary integer program toevaluate a number of potential locations for new warehouses. Thefirm’s goal is to maximize the net present value of their decisionwhile 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}

x j ={ 1, if location j is selected 0, otherwise xj=1, iflocation j is selected0, otherwise

Solve this problem to optimality and answer the followingquestions:

A. What is the net present value of the optimal solution? (Roundyour answer to the nearest whole number.)

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

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