Explanation Given information: The objective function which has to maximize is: z = 2 x + 3 y which is subjected to the constraints: { x + 2 y ≤ 14 x + y ≤ 9 3 x + 2 y ≤ 24 x ≥ 0 y ≥ 0 Formula used: The duality of primal problem can be determined as below: If the primal problem is in the form: Maximize: z = a x + b y , which is subjected to constraints: { a 1 x + b 1 y ≤ c 1 a 2 x + b 2 y ≤ c 2 x ≥ 0 y ≥ 0 In matrix form, the objective function is: Maximize: z = [ a b ] [ x y ] And, constraints are: A X ≤ C [ a 1 b 1 a 2 b 2 ] [ x y ] ≤ [ c 1 c 2 ] Then its dual is: Minimize: z = [ c 1 c 2 ] [ u v ] And, constraints are: A T U ≥ B [ a 1 a 2 b 1 b 2 ] [ u v ] ≥ [ a b ] And, if the primal problem is in the form: Minimize: z = a x + b y , which is subjected to constraints: { a 1 x + b 1 y ≥ c 1 a 2 x + b 2 y ≥ c 2 x ≥ 0 y ≥ 0 In matrix form, the objective function is: Minimize: z = [ a b ] [ x y ] And, constraints are: A X ≥ C [ a 1 b 1 a 2 b 2 ] [ x y ] ≥ [

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134507125

Author: Goldstein

Publisher: PEARSON

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Chapter 4, Problem 11RE

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To calculate: The dual problem of maximization problem which has objective function: z=2x+3y which is subjected to the constraints:

{x+2y≤14x+y≤93x+2y≤24x≥0y≥0

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Chapter 4, Problem 10RE

Chapter 4, Problem 12RE

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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 maximization problem which has objective function: z = 2 x + 3 y which is subjected to the constraints: { x + 2 y ≤ 14 x + y ≤ 9 3 x + 2 y ≤ 24 x ≥ 0 y ≥ 0

Solution Summary: The author explains that the objective function of the primal problem is: Maximize: z=2x+3y, which is subjected to constraints.

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To calculate: The dual problem of maximization problem which has objective function: z=2x+3y which is subjected to the constraints:

{x+2y≤14x+y≤93x+2y≤24x≥0y≥0

Want to see the full answer?

Chapter 4 Solutions

The dual problem of maximization problem which has objective function: z = 2 x + 3 y which is subjected to the constraints: { x + 2 y ≤ 14 x + y ≤ 9 3 x + 2 y ≤ 24 x ≥ 0 y ≥ 0

Solution Summary: The author explains that the objective function of the primal problem is: Maximize: z=2x+3y, which is subjected to constraints.

Videos

To calculate: The dual problem of maximization problem which has objective function: z=2x+3y which is subjected to the constraints: {x+2y≤14x+y≤93x+2y≤24x≥0y≥0

Want to see the full answer?

Chapter 4 Solutions

To calculate: The dual problem of maximization problem which has objective function: z=2x+3y which is subjected to the constraints:

{x+2y≤14x+y≤93x+2y≤24x≥0y≥0