Explanation Given Information: The provided linear programming problem is, Minimize 21 x + 14 y subject to the constraints { 15 x + 22.5 y ≥ 90 810 x + 270 y ≥ 1620 1 9 x + 1 3 y ≥ 1 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 21 x + 14 y subject to the constraints { 15 x + 22.5 y ≥ 90 810 x + 270 y ≥ 1620 1 9 x + 1 3 y ≥ 1 x ≥ 0 , y ≥ 0 First write the provided linear programming problem into standard form. Minimize [ 21 14 ] [ x y ] subject to the constraints [ 15 22.5 810 270 1 9 1 3 ] [ x y ] ≥ [ 90 1620 1 ] and [ x y ] ≥ [ 0 0 ] Suppose that one can supply the nutrients some other way, at a cost of u cents per gram of protein, v cents per calorie and w cents per milligram of riboflavin. To find the maximum cost at which this can be done, find 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 [ 21 14 ] [ x y ] subject to the constraints [ 15 22.5 810 270 1 9 1 3 ] [ x y ] ≥ [ 90 1620 1 ] and [ x y ] ≥ [ 0 0 ] ” with the statement “Minimize CX subject to the constraints A X ≥ B , X ≥ 0 ”. It can be seen that C = [ 21 14 ] , A = [ 15 22

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 18E

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

Minimize 21x+14y subject to the constraints {15x+22.5y≥90810x+270y≥162019x+13y≥1x≥0,y≥0

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Chapter 4.5, Problem 17E

Chapter 4.5, Problem 19E

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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 21 x + 14 y subject to the constraints { 15 x + 22.5 y ≥ 90 810 x + 270 y ≥ 1620 1 9 x + 1 3 y ≥ 1 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 21x+14y subject to the constraints {15x+22.5y≥90810x+270y≥162019x+13y≥1x≥0,y≥0

Want to see the full answer?

Chapter 4 Solutions

The economic interpretation to the dual of the linear programming problem, Minimize 21 x + 14 y subject to the constraints { 15 x + 22.5 y ≥ 90 810 x + 270 y ≥ 1620 1 9 x + 1 3 y ≥ 1 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 21x+14y subject to the constraints {15x+22.5y≥90810x+270y≥162019x+13y≥1x≥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 21x+14y subject to the constraints {15x+22.5y≥90810x+270y≥162019x+13y≥1x≥0,y≥0