Explanation Given Information: The provided linear programming problem is, Minimize 3 x + 5 y + z subject to the constraints { 2 x − 4 y − 6 z ≤ 7 y ≥ 10 − 8 x − 9 z x ≥ 0 , y ≥ 0 , z ≥ 0 . Consider the provided linear programming problem, Minimize 3 x + 5 y + z subject to the constraints { 2 x − 4 y − 6 z ≤ 7 y ≥ 10 − 8 x − 9 z x ≥ 0 , y ≥ 0 , z ≥ 0 . First write the provided linear programming problem into standard form. Minimize [ 3 5 1 ] [ x y z ] subject to the constraints [ 2 − 4 − 6 − 8 − 1 − 9 ] [ x y z ] ≤ [ 7 − 10 ] and [ x y z ] ≥ [ 0 0 0 ] Now, if the original (primal) problem has the 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 . So, compare the statement, “Minimize [ 3 5 1 ] [ x y z ] subject to the constraints [ − 2 4 6 8 1 9 ] [ x y z ] ≥ [ − 7 10 ] and [ x y z ] ≥ [ 0 0 0 ] ” with the statement “Minimize CX subject to the constraints A X ≥ B , X ≥ 0 ”. It can be seen that C = [ 3 5 1 ] , A = [ − 2 4 6 8 1 9 ] , B = [ − 7 10 ] and X = [ x y z ]

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 5E

To determine

The dual problem of the linear programming problem,

Minimize 3x+5y+z subject to the constraints,

{2x−4y−6z≤7y≥10−8x−9zx≥0,y≥0,z≥0

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Chapter 4.5, Problem 4E

Chapter 4.5, Problem 6E

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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 3 x + 5 y + z subject to the constraints, { 2 x − 4 y − 6 z ≤ 7 y ≥ 10 − 8 x − 9 z x ≥ 0 , y ≥ 0 , z ≥ 0

Solution Summary: The author explains that the provided linear programming problem is, Minimize 3x+5y+z subject to the constraints.

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The dual problem of the linear programming problem,

Minimize 3x+5y+z subject to the constraints,

{2x−4y−6z≤7y≥10−8x−9zx≥0,y≥0,z≥0

Want to see the full answer?

Chapter 4 Solutions

The dual problem of the linear programming problem, Minimize 3 x + 5 y + z subject to the constraints, { 2 x − 4 y − 6 z ≤ 7 y ≥ 10 − 8 x − 9 z x ≥ 0 , y ≥ 0 , z ≥ 0

Solution Summary: The author explains that the provided linear programming problem is, Minimize 3x+5y+z subject to the constraints.

Videos

The dual problem of the linear programming problem, Minimize 3x+5y+z subject to the constraints, {2x−4y−6z≤7y≥10−8x−9zx≥0,y≥0,z≥0

Want to see the full answer?

Chapter 4 Solutions

The dual problem of the linear programming problem,

Minimize 3x+5y+z subject to the constraints,

{2x−4y−6z≤7y≥10−8x−9zx≥0,y≥0,z≥0