Explanation Given Information: The provided linear programming problem is, Minimize 30 x + 60 y + 50 z subject to the constraints: { 5 x + 3 y + z ≥ 2 x + 2 y + z ≥ 3 x ≥ 0 , y ≥ 0 , z ≥ 0 Formula Used: If the primal problem is of form: Minimize CX subject to the constraints A X ≥ B , X ≥ 0 , then the dual problem is: Maximize B T U subject to the constraints A T U ≤ C T , U ≥ 0 . Calculation: Consider the provided linear programming problem, Minimize 30 x + 60 y + 50 z subject to the constraints: { 5 x + 3 y + z ≥ 2 x + 2 y + z ≥ 3 x ≥ 0 , y ≥ 0 , z ≥ 0 The primal problem can be written in the form of: Minimize [ 30 60 50 ] [ x y z ] subject to the constraints: [ 5 3 1 1 2 1 ] [ x y z ] ≥ [ 2 3 ] and [ x y z ] ≥ [ 0 0 0 ] Compare the above statement with the statement “Minimize CX subject to the constraints A X ≥ B , X ≥ 0 ”

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134437767

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

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Chapter 4.5, Problem 2E

To determine

To calculate: The dual problem of the linear programming problem:

Minimize 30x+60y+50z subject to the constraints:

{5x+3y+z≥2x+2y+z≥3x≥0,y≥0,z≥0

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Chapter 4.5, Problem 1E

Chapter 4.5, Problem 3E

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Chapter 4 Solutions

Finite Mathematics & Its Applications (12th Edition)

Ch. 4.1 - 1. Determine by inspection a particular solution...Ch. 4.1 - Prob. 2CYU Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - 712For each of the linear programming problems in...Ch. 4.1 - 7–12 For each of the linear programming problems...

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The dual problem of the linear programming problem: Minimize 30 x + 60 y + 50 z subject to the constraints: { 5 x + 3 y + z ≥ 2 x + 2 y + z ≥ 3 x ≥ 0 , y ≥ 0 , z ≥ 0

Solution Summary: The author calculates the dual problem of the linear programming problem: Minimize 30x+60y+50z subject to the constraints.

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To calculate: The dual problem of the linear programming problem:

Minimize 30x+60y+50z subject to the constraints:

{5x+3y+z≥2x+2y+z≥3x≥0,y≥0,z≥0

Want to see the full answer?

Chapter 4 Solutions

The dual problem of the linear programming problem: Minimize 30 x + 60 y + 50 z subject to the constraints: { 5 x + 3 y + z ≥ 2 x + 2 y + z ≥ 3 x ≥ 0 , y ≥ 0 , z ≥ 0

Solution Summary: The author calculates the dual problem of the linear programming problem: Minimize 30x+60y+50z subject to the constraints.

Videos

To calculate: The dual problem of the linear programming problem: Minimize 30x+60y+50z subject to the constraints: {5x+3y+z≥2x+2y+z≥3x≥0,y≥0,z≥0

Want to see the full answer?

Chapter 4 Solutions

To calculate: The dual problem of the linear programming problem:

Minimize 30x+60y+50z subject to the constraints:

{5x+3y+z≥2x+2y+z≥3x≥0,y≥0,z≥0