Explanation Given Information: The provided function as: Minimize c = 0.2 s + 0.3 t . Subject to s ≥ 0 , t ≥ 0 , s + t ≥ 8 , s + 2 t ≥ 10 and 2 s + t ≥ 10 . Formula used: Formula for the two LP problem one for minimization and second is the maximization and the transpose of the matrix represent the duality. Step1: To find the duality of a provided problem as follows: (a): Transform the problem into matrix. (b): Perform transpose of the matrix. (c): Write the one of two required for the LP problem one for minimization or second is the maximization. The primal problem is called as original problem and its dual can be said as dual problem. Step2: Apply the simplex method to solve the dual problem that are provided. Step3: At last divide the associated value of the slack variables by the entry in the p column of the table to find the final result. Calculation: Consider the provided function as: Minimize c = 0.2 s + 0.3 t . Subject to s ≥ 0 , t ≥ 0 , s + t ≥ 8 , s + 2 t ≥ 10 and 2 s + t ≥ 10 . Represent this above problem by the matrix as: [ 2 1 10 1 2 10 1 0.2 1 0.3 8 0 ] Now taking the transpose of the matrix as: [ 2 1 10 1 2 10 1 1 8 0.2 0.3 0 ] Now, write down the dual, which is the LP problem corresponding to the new matrix as: Maximize p = 10 x + 10 y + 8 z . Subject to x ≥ 0 , y ≥ 0 , 2 x + y + z ≤ 0.2 and x + 2 y + z ≤ 0.3 . Solve the dual problem using the standard simplex method as: x y z s t p s 2 1 1 1 0 0 0.2 t 1 2 1 0 1 0 0.3 p − 20 − 20 0 0 3 0 1 0 Apply row operation, 5 R − 1 and 10 R − 2

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 6.5, Problem 13E

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

Minimize c=0.2s+0.3t.

Subject to s≥0,t≥0, s+t≥8, s+2t≥10 and 2s+t≥10.

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Chapter 6.5, Problem 12E

Chapter 6.5, Problem 14E

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The standard minimization by the use of duality minimizes the provided equation. Minimize c = 0.2 s + 0.3 t . Subject to s ≥ 0 , t ≥ 0 , s + t ≥ 8 , s + 2 t ≥ 10 and 2 s + t ≥ 10 .

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=0.2s+0.3t.

Subject to s≥0,t≥0, s+t≥8, s+2t≥10 and 2s+t≥10.

Want to see the full answer?

Chapter 6 Solutions

The standard minimization by the use of duality minimizes the provided equation. Minimize c = 0.2 s + 0.3 t . Subject to s ≥ 0 , t ≥ 0 , s + t ≥ 8 , s + 2 t ≥ 10 and 2 s + t ≥ 10 .

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

Videos

To calculate: The standard minimization by the use of duality minimizes the provided equation. Minimize c=0.2s+0.3t. Subject to s≥0,t≥0, s+t≥8, s+2t≥10 and 2s+t≥10.

Want to see the full answer?

Chapter 6 Solutions

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

Minimize c=0.2s+0.3t.

Subject to s≥0,t≥0, s+t≥8, s+2t≥10 and 2s+t≥10.