Explanation Given Information: Provided the optimization problem with mixed constraint is: Maximize f = 4 x + y subject to 3 x + 2 y ≤ 12 3 x − 4 y ≥ 6 x ≥ 0 , y ≥ 0 Formula used: In an optimization problem, if a constraint has the form a 1 x 1 + a 2 x 2 + ... + a n x n ≥ b , where b ≥ 0 . To convert it into standard form of ≤ , multiplying both sides of the inequality by ( − 1 ) . a 1 x 1 + a 2 x 2 + ... + a n x n ≥ b Becomes − a 1 x 1 − a 2 x 2 − ... + a n x n ≤ − b . To form simplex matrix, convert all constraints as ≤ constraints and add slack variable into inequality to convert it into equality. Write all equations in a matrix form that is simplex matrix. Calculation: Provided the linear programming problem is Maximize f = 4 x + y subject to 3 x + 2 y ≤ 12 3 x − 4 y ≥ 6 x ≥ 0 , y ≥ 0 Express all constraints as ≤ constraints. To form the simplex form, convert all the inequalities into equations, add slack variable into the inequalities. 3 x − 4 y ≥ 6 Multiple above constraint by ( − 1 ) both sides

Mathematical Applications for the Management, Life, and Social Sciences

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ISBN: 9781305108042

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 4.5, Problem 1CP

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To calculate: The simplex matrix of the given linear programing problem.

Maximize f=4x+y subject to3x+2y≤123x−4y≥6x≥0,y≥0

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Chapter 4.4, Problem 34E

Chapter 4.5, Problem 2CP

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The simplex matrix of the given linear programing problem. Maximize f = 4 x + y subject to 3 x + 2 y ≤ 12 3 x − 4 y ≥ 6 x ≥ 0 , y ≥ 0

Solution Summary: The author explains how to calculate the simplex matrix of a linear programing problem.

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To calculate: The simplex matrix of the given linear programing problem.

Maximize f=4x+y subject to3x+2y≤123x−4y≥6x≥0,y≥0

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Chapter 4 Solutions

The simplex matrix of the given linear programing problem. Maximize f = 4 x + y subject to 3 x + 2 y ≤ 12 3 x − 4 y ≥ 6 x ≥ 0 , y ≥ 0

Solution Summary: The author explains how to calculate the simplex matrix of a linear programing problem.

Videos

To calculate: The simplex matrix of the given linear programing problem. Maximize f=4x+y subject to3x+2y≤123x−4y≥6x≥0,y≥0

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Chapter 4 Solutions

To calculate: The simplex matrix of the given linear programing problem.

Maximize f=4x+y subject to3x+2y≤123x−4y≥6x≥0,y≥0