Explanation Given Information: The provided equation is, Maximize p = x + y + z + w Subject to x + y + z ≤ 3 , y + z + w ≤ 3 , x + z + w ≤ 4 , x + y + w ≤ 4 and x ≥ 0 , y ≥ 0 , z ≥ 0 , w ≥ 0 Formula used: Two LP problems, one is a maximization and other is minimization problem are dual if the matrix that represent one is the transpose of the transpose of the other matrix. Step1: Finding the dual of a given problem follows: (a): represent the problem in a matrix form. (b): Take the transpose of the matrix. (c): Write down the dual, which is the LP problem corresponding to the new matrix. If the original problem was a maximization problem then its dual will be a minimization problem and vice versa. The original problem is called as the primal problem, and its dual is called to as the dual problem. Calculation: Consider the provided equation, Maximize p = x + y + z + w Subject to x + y + z ≤ 3 , y + z + w ≤ 3 , x + z + w ≤ 4 , x + y + w ≤ 4 and x ≥ 0 , y ≥ 0 , z ≥ 0 , w ≥ 0 Represent this above problem by the matrix as: [ 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 3 3

7th Edition

ISBN: 9781337515542

Author: Waner

Publisher: Cengage

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Chapter 5.5, Problem 6E

To determine

To calculate: The dual LP program of the provided equation,

Maximize p=x+y+z+w

Subject to x+y+z≤3,y+z+w≤3,x+z+w≤4,x+y+w≤4 and x≥0,y≥0,z≥0,w≥0

Expert Solution & Answer

Chapter 5 Solutions

Finite Mathematics

Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - Prob. 6E Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - In Exercises 1-26, sketch the region that...Ch. 5.1 - Prob. 9E Ch. 5.1 - In Exercises 1-26, sketch the region that...

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The dual LP program of the provided equation, Maximize p = x + y + z + w Subject to x + y + z ≤ 3 , y + z + w ≤ 3 , x + z + w ≤ 4 , x + y + w ≤ 4 and x ≥ 0 , y ≥ 0 , z ≥ 0 , w ≥ 0

Solution Summary: The author calculates the dual LP program of the provided equation, Maximize p=x+y+z+w.

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To calculate: The dual LP program of the provided equation,

Maximize p=x+y+z+w

Subject to x+y+z≤3,y+z+w≤3,x+z+w≤4,x+y+w≤4 and x≥0,y≥0,z≥0,w≥0

Chapter 5 Solutions

The dual LP program of the provided equation, Maximize p = x + y + z + w Subject to x + y + z ≤ 3 , y + z + w ≤ 3 , x + z + w ≤ 4 , x + y + w ≤ 4 and x ≥ 0 , y ≥ 0 , z ≥ 0 , w ≥ 0

Solution Summary: The author calculates the dual LP program of the provided equation, Maximize p=x+y+z+w.

Videos

To calculate: The dual LP program of the provided equation, Maximize p=x+y+z+w Subject to x+y+z≤3,y+z+w≤3,x+z+w≤4,x+y+w≤4 and x≥0,y≥0,z≥0,w≥0

Chapter 5 Solutions

To calculate: The dual LP program of the provided equation,

Maximize p=x+y+z+w

Subject to x+y+z≤3,y+z+w≤3,x+z+w≤4,x+y+w≤4 and x≥0,y≥0,z≥0,w≥0