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

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}

x j ={ 1, if location j is selected 0, otherwise xj=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)? (Round your answer to the nearest whole number.)

Solutions

Expert Solution

Answer Report:

A) 30

B) 17

Colby Messinger answered 1 year ago

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