b. What is the net present value of the optimal solution? (Round your answer to the nearest whole number.)Net present valuec. How much of the available capital will be spent (Hint: Constraint 1enforces the available capital limit)? (Round your answer to thenearest whole number.)Available capital A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm'sgoal is to maximize the net present value of their decision while not spending more than their currently available capital.Max 35x1 + 35x2 + 20x3+ 30x4s.t. 12x1 + 10x2 + 4x3 + 13x4 < 18 {Constraint 1}x1 + x2X4 2 2 (Constraint 2}+X3x1+ x2 3 1 (Constraint 3]x1+ x3 2 1 {Constraint 4}x2 = x4 (Constraint 5)1, if location jis selected0, otherwiseSolve this problem to optimality and answer the following questions:a. Which of the warehouse locations will/will not be selected?Location 1 willLocation 2 willLocation 3 willLocation 4 will

Answered: Image /qna-images/answer/663d611b-1d9c-4809-835b-0b91f9ce45a5.jpg

Answered: A firm has prepared the following…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 80P

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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 15x1 + 15x2 + 15x3+ 30x4s.t. 7x1 + 13x2 + 11x3 + 10x4 ≤ 20 {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, otherwise Solve this problem to optimality and answer the following questions: Which of the warehouse locations will/will not be selected?
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 15x1 + 25x2 + 15x3+ 35x4s.t. 8x1 + 11x2 + 6x3 + 6x4 ≤ 17 {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: Which of the warehouse locations will/will not be selected? What is the net present value of the optimal solution? (Round your answer to the nearest whole number.) 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.)
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