Explanation Given Information: The provided function as: Minimize c = s + 2 t Subject to s + 3 t ≥ 30 , 2 s + t ≥ 30 and s ≥ 0 , t ≥ 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. Step2: Use the simplex method to solve the dual problem. Step3: Read off the solution to the primal problem by dividing the bottom entries into the columns associated with the slack variables by the entry in the p column. Calculation: Consider the provided function as: Minimize c = s + 2 t Subject to s + 3 t ≥ 30 , 2 s + t ≥ 30 and s ≥ 0 , t ≥ 0 . Represent this above problem by the matrix as: [ 1 3 30 2 1 30 1 2 0 ] Now taking the transpose of the matrix as: [ 1 2 1 3 1 2 30 30 0 ] Now, write down the dual, which is the LP problem corresponding to the new matrix as: Maximize p = 30 x + 30 y Subject to x + 2 y ≤ 1 , 3 x + y ≤ 2 and x ≥ 0 , y ≥ 0 Solve the dual problem using the standard simplex method as: x y s t p s 1 2 1 0

Finite Mathematics and Application Calculus (Looseleaf) - Text Only

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ISBN: 9781337291484

Author: Waner

Publisher: Cengage

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Chapter 6.5, Problem 10E

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To calculate: The standard minimization by the use of duality minimizes the provided equation.

Minimize c=s+2t

Subject to s+3t≥30,2s+t≥30 and s≥0,t≥0.

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Chapter 6.5, Problem 9E

Chapter 6.5, Problem 11E

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Finite Mathematics and Application Calculus (Looseleaf) - Text Only

Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

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The standard minimization by the use of duality minimizes the provided equation. Minimize c = s + 2 t Subject to s + 3 t ≥ 30 , 2 s + t ≥ 30 and s ≥ 0 , t ≥ 0 .

Solution Summary: The author explains how the standard minimization by the use of duality minimizes the provided equation.

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To calculate: The standard minimization by the use of duality minimizes the provided equation.

Minimize c=s+2t

Subject to s+3t≥30,2s+t≥30 and s≥0,t≥0.

Want to see the full answer?

Chapter 6 Solutions

The standard minimization by the use of duality minimizes the provided equation. Minimize c = s + 2 t Subject to s + 3 t ≥ 30 , 2 s + t ≥ 30 and s ≥ 0 , t ≥ 0 .

Solution Summary: The author explains how the standard minimization by the use of duality minimizes the provided equation.

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To calculate: The standard minimization by the use of duality minimizes the provided equation. Minimize c=s+2t Subject to s+3t≥30,2s+t≥30 and s≥0,t≥0.

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Chapter 6 Solutions

To calculate: The standard minimization by the use of duality minimizes the provided equation.

Minimize c=s+2t

Subject to s+3t≥30,2s+t≥30 and s≥0,t≥0.