A linear programming problem is given as follows: maximize ? = 50x1 + 80x2 + 64x3 + 80x4Subject to 5x1 +2.5x2+ 4.5x3+ 3.99x4 ≤ 6004.1x1 +2.6x2+ 5.5x3+ 1.9x4 ≤ 50015x1 +22x2+ 18x3+ 25x4 ≤ 4008x1 +12.6x2+ 9.7x3+ 10.55x4 ≤ 1700x1 + x2 / x1 + x2 + x3 + x4 ≥ 0.60x1, x2, x3, x4 ≥ 0

Here, we would maximize the objective value, Maximize the Objective function =50x1 + 80x2 + 64x3 +…

Answered: A linear programming problem is given…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 76P

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Question

A linear programming problem is given as follows:

maximize ? = 50x₁ + 80x₂ + 64x₃ + 80x₄

Subject to 5x₁ +

2.5x₂

+ 4.5x₃

+ 3.99x₄ ≤ 600

4.1x₁ +

2.6x₂

+ 5.5x₃

+ 1.9x₄ ≤ 500

15x₁ +

22x₂

+ 18x₃

+ 25x₄ ≤ 400

8x₁ +

12.6x₂

+ 9.7x₃

+ 10.55x₄ ≤ 1700

x₁ + x_{2 /}x₁ + x₂ + x₃ + x₄≥ 0.60

x_1, x₂, x₃, x₄ ≥ 0

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This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.

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