Explanation Given information: The production is given by Q = 5 x 0.3 y 0.8 , x and y are the quantities of the raw materials and total quantity of the raw material cannot go beyond 100 . Formula used: Method of Langrage multiplier, Step 1- Consider the multivariable production function f ( x , y ) Step 2- Formulate the constraint function Step 3- From first derivative method obtain the equations with the help of Langrage multiplier λ Step 4- Solve the equation and find the values of the labor input and capital input Step 5- Dictate the answer Calculation: Consider the information that the production is given by Q = 5 x 0.3 y 0.8 , x and y are the quantities of the raw materials and total quantity of the raw material cannot go beyond 100 . The constraint function to the quantity function is x + y = 100 . Find the first derivatives of the functions as below. Q x ( x , y ) = 1.5 x − 0.7 y 0.8 … ( 1 ) Q y ( x , y ) = 4 x 0.3 y − 0.2 … ( 2 ) C x ( x , y ) = 1 … ( 3 ) C y ( x , y ) = 1 … ( 4 ) Use the langrage multipliers to formulate the relations between production function and constraint values as below. 1.5 x − 0

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ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 8.6, Problem 19P

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The maximize production of the goods while the production is given by Q=5x0.3y0.8, x and y are the quantities of the raw materials and total quantity of the raw material cannot go beyond 100.

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Chapter 8.6, Problem 18P

Chapter 8.6, Problem 20P

Chapter 8 Solutions

APPLIED CALCULUS (WILEY PLUS)

Ch. 8.1 - Prob. 1P Ch. 8.1 - Prob. 2P Ch. 8.1 - Prob. 3P Ch. 8.1 - Prob. 4P Ch. 8.1 - Prob. 5P Ch. 8.1 - Prob. 6P Ch. 8.1 - Prob. 7P Ch. 8.1 - Prob. 8P Ch. 8.1 - Prob. 9P Ch. 8.1 - Prob. 10P

Ch. 8.1 - Prob. 11P Ch. 8.1 - Prob. 12P Ch. 8.1 - Prob. 13P Ch. 8.1 - Prob. 14P Ch. 8.1 - Prob. 15P Ch. 8.1 - Prob. 16P Ch. 8.1 - Prob. 17P Ch. 8.1 - Prob. 18P Ch. 8.1 - Prob. 19P Ch. 8.1 - Prob. 20P Ch. 8.1 - Prob. 21P Ch. 8.1 - Prob. 22P Ch. 8.1 - Prob. 23P Ch. 8.1 - Prob. 24P Ch. 8.1 - Prob. 25P Ch. 8.1 - Prob. 26P Ch. 8.1 - Prob. 27P Ch. 8.1 - Prob. 28P Ch. 8.1 - Prob. 29P Ch. 8.1 - Prob. 30P Ch. 8.2 - Prob. 1P Ch. 8.2 - Prob. 2P Ch. 8.2 - Prob. 3P Ch. 8.2 - Prob. 4P Ch. 8.2 - Prob. 5P Ch. 8.2 - Prob. 6P Ch. 8.2 - Prob. 7P Ch. 8.2 - Prob. 8P Ch. 8.2 - Prob. 9P Ch. 8.2 - Prob. 10P Ch. 8.2 - Prob. 11P Ch. 8.2 - Prob. 12P Ch. 8.2 - Prob. 13P Ch. 8.2 - Prob. 14P Ch. 8.2 - Prob. 15P Ch. 8.2 - Prob. 16P Ch. 8.2 - Prob. 17P Ch. 8.2 - Prob. 18P Ch. 8.2 - Prob. 19P Ch. 8.2 - Prob. 20P Ch. 8.2 - Prob. 21P Ch. 8.2 - Prob. 22P Ch. 8.2 - Prob. 23P Ch. 8.2 - Prob. 24P Ch. 8.2 - Prob. 25P Ch. 8.2 - Prob. 26P Ch. 8.2 - Prob. 27P Ch. 8.2 - Prob. 28P Ch. 8.2 - Prob. 29P Ch. 8.2 - Prob. 30P Ch. 8.2 - 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Prob. 38P Ch. 8.3 - Prob. 39P Ch. 8.3 - Prob. 40P Ch. 8.4 - Prob. 1P Ch. 8.4 - Prob. 2P Ch. 8.4 - Prob. 3P Ch. 8.4 - Prob. 4P Ch. 8.4 - Prob. 5P Ch. 8.4 - Prob. 6P Ch. 8.4 - Prob. 7P Ch. 8.4 - Prob. 8P Ch. 8.4 - Prob. 9P Ch. 8.4 - Prob. 10P Ch. 8.4 - Prob. 11P Ch. 8.4 - Prob. 12P Ch. 8.4 - Prob. 13P Ch. 8.4 - Prob. 14P Ch. 8.4 - Prob. 15P Ch. 8.4 - Prob. 16P Ch. 8.4 - Prob. 17P Ch. 8.4 - Prob. 18P Ch. 8.4 - Prob. 19P Ch. 8.4 - Prob. 20P Ch. 8.4 - Prob. 21P Ch. 8.4 - Prob. 22P Ch. 8.4 - Prob. 23P Ch. 8.4 - Prob. 24P Ch. 8.4 - Prob. 25P Ch. 8.4 - Prob. 26P Ch. 8.4 - Prob. 27P Ch. 8.4 - Prob. 28P Ch. 8.4 - Prob. 29P Ch. 8.4 - Prob. 30P Ch. 8.4 - Prob. 31P Ch. 8.4 - Prob. 32P Ch. 8.4 - Prob. 33P Ch. 8.4 - Prob. 34P Ch. 8.4 - Prob. 35P Ch. 8.4 - Prob. 36P Ch. 8.4 - Prob. 37P Ch. 8.4 - Prob. 38P Ch. 8.4 - Prob. 39P Ch. 8.4 - Prob. 40P Ch. 8.4 - Prob. 41P Ch. 8.4 - Prob. 42P Ch. 8.4 - Prob. 43P Ch. 8.4 - Prob. 44P Ch. 8.5 - Prob. 1P Ch. 8.5 - Prob. 2P Ch. 8.5 - Prob. 3P Ch. 8.5 - Prob. 4P Ch. 8.5 - 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The maximize production of the goods while the production is given by Q = 5 x 0.3 y 0.8 , x and y are the quantities of the raw materials and total quantity of the raw material cannot go beyond 100 .

Solution Summary: The author calculates the maximum production of the goods for x=27andy=73.

Videos

To calculate:

The maximize production of the goods while the production is given by Q=5x0.3y0.8, x and y are the quantities of the raw materials and total quantity of the raw material cannot go beyond 100.

Want to see the full answer?

Chapter 8 Solutions

The maximize production of the goods while the production is given by Q = 5 x 0.3 y 0.8 , x and y are the quantities of the raw materials and total quantity of the raw material cannot go beyond 100 .

Solution Summary: The author calculates the maximum production of the goods for x=27andy=73.

Videos

To calculate: The maximize production of the goods while the production is given by Q=5x0.3y0.8, x and y are the quantities of the raw materials and total quantity of the raw material cannot go beyond 100.

Want to see the full answer?

Chapter 8 Solutions

To calculate:

The maximize production of the goods while the production is given by Q=5x0.3y0.8, x and y are the quantities of the raw materials and total quantity of the raw material cannot go beyond 100.