Explanation Given Information: The provided linear programming problem is, Minimize 150 x + 200 y subject to the constraints { 4 x + 10 y ≥ 80 4 x + 5 y ≥ 60 7 x + 5 y ≥ 75 x ≥ 0 , y ≥ 0 Formula used: The dual of a linear programming problem: 1. If the original (primal) problems has the form Maximize CX subject to the constraints A X ≤ B , X ≥ 0 , then the dual problem is, Minimize B T U subject to the constraints A T U ≥ C T , U ≥ 0 . 2. If the original (primal) problems 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 . Calculation: Consider the provided linear programming problem, Minimize 150 x + 200 y subject to the constraints { 4 x + 10 y ≥ 80 4 x + 5 y ≥ 60 7 x + 5 y ≥ 75 x ≥ 0 , y ≥ 0 First write the provided linear programming problem into standard form. Minimize [ 150 200 ] [ x y ] subject to the constraints [ 4 10 4 5 7 5 ] [ x y ] ≥ [ 80 60 75 ] and [ x y ] ≥ [ 0 0 ] Suppose that one can buy anthracite at u dollars per ton, ordinary coal at v dollars per ton and bituminous coal at w dollars per ton. To find the maximum cost at which this can be done, find the dual of the original problem. 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 [ 150 200 ] [ x y ] subject to the constraints [ 4 10 4 5 7 5 ] [ x y ] ≥ [ 80 60 75 ] and [ x y ] ≥ [ 0 0 ] ” 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 17E

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To calculate: The economic interpretation to the dual of the linear programming problem,

Minimize 150x+200y subject to the constraints {4x+10y≥804x+5y≥607x+5y≥75x≥0,y≥0

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Chapter 4.5, Problem 16E

Chapter 4.5, Problem 18E

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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 economic interpretation to the dual of the linear programming problem, Minimize 150 x + 200 y subject to the constraints { 4 x + 10 y ≥ 80 4 x + 5 y ≥ 60 7 x + 5 y ≥ 75 x ≥ 0 , y ≥ 0

Solution Summary: The author calculates the economic interpretation to the dual of the linear programming problem.

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To calculate: The economic interpretation to the dual of the linear programming problem,

Minimize 150x+200y subject to the constraints {4x+10y≥804x+5y≥607x+5y≥75x≥0,y≥0

Want to see the full answer?

Chapter 4 Solutions

The economic interpretation to the dual of the linear programming problem, Minimize 150 x + 200 y subject to the constraints { 4 x + 10 y ≥ 80 4 x + 5 y ≥ 60 7 x + 5 y ≥ 75 x ≥ 0 , y ≥ 0

Solution Summary: The author calculates the economic interpretation to the dual of the linear programming problem.

Videos

To calculate: The economic interpretation to the dual of the linear programming problem, Minimize 150x+200y subject to the constraints {4x+10y≥804x+5y≥607x+5y≥75x≥0,y≥0

Want to see the full answer?

Chapter 4 Solutions

To calculate: The economic interpretation to the dual of the linear programming problem,

Minimize 150x+200y subject to the constraints {4x+10y≥804x+5y≥607x+5y≥75x≥0,y≥0