Explanation Given Information: The provided equation is, Minimize c = 5 s + 2 u + v Subject to s − t + 2 v ≥ 2000 , u + v ≤ 3000 , s + t ≥ 500 and s ≥ 0 , t ≥ 0 , u ≥ 0 , v ≥ 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, Minimize c = 5 s + 2 u + v Subject to s − t + 2 v ≥ 2000 , u + v ≤ 3000 , s + t ≥ 500 and s ≥ 0 , t ≥ 0 , u ≥ 0 , v ≥ 0 Represent this above problem by the matrix as: [ 1 − 1 0 2 0 0 1 1 1 1 0 0 5 0 2 1 2 , 000

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ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 5.5, Problem 8E

To determine

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

Minimize c=5s+2u+v

Subject to s−t+2v≥2000, u+v≤3000,s+t≥500 and s≥0,t≥0,u≥0,v≥0

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Chapter 5.5, Problem 7E

Chapter 5.5, Problem 9E

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The dual LP program of the provided equation, Minimize c = 5 s + 2 u + v Subject to s − t + 2 v ≥ 2000 , u + v ≤ 3000 , s + t ≥ 500 and s ≥ 0 , t ≥ 0 , u ≥ 0 , v ≥ 0

Solution Summary: The author calculates the dual LP program of the provided equation, Minimize c=5s+2u+v.

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

Minimize c=5s+2u+v

Subject to s−t+2v≥2000, u+v≤3000,s+t≥500 and s≥0,t≥0,u≥0,v≥0

Want to see the full answer?

Chapter 5 Solutions

The dual LP program of the provided equation, Minimize c = 5 s + 2 u + v Subject to s − t + 2 v ≥ 2000 , u + v ≤ 3000 , s + t ≥ 500 and s ≥ 0 , t ≥ 0 , u ≥ 0 , v ≥ 0

Solution Summary: The author calculates the dual LP program of the provided equation, Minimize c=5s+2u+v.

Videos

To calculate: The dual LP program of the provided equation, Minimize c=5s+2u+v Subject to s−t+2v≥2000, u+v≤3000,s+t≥500 and s≥0,t≥0,u≥0,v≥0

Want to see the full answer?

Chapter 5 Solutions

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

Minimize c=5s+2u+v

Subject to s−t+2v≥2000, u+v≤3000,s+t≥500 and s≥0,t≥0,u≥0,v≥0