Explanation Given Information: The productivity model at the company is P = 10 , 000 x 0.7 y 0.3 , P is the number of gadgets the company turns out per month, x is the number of employees at the company and y is the monthly operating budget in thousands of dollars, the number of workers is between 45 and 55 . The operating budget varies from $ 8 , 000 to $ 12 , 000 per month. Formula used: The value of the integral ∬ R f ( x , y ) d x d y is ∫ a b ( ∫ c ( x ) d ( x ) f ( x , y ) d y ) d x where the region R is defined by a ≤ x ≤ b and c ( x ) ≤ y ≤ d ( x ) . The average value of a function f ( x , y ) on the region R is f ¯ = 1 A ∬ R f ( x , y ) d x d y where A is the area of the region, A = ∬ R d x d y . Calculation: Consider the productivity model at the company is P = 10 , 000 x 0.3 y 0.7 , P is the number of gadgets the company turns out per month, x is the number of employees at the company and y is the monthly operating budget in thousands of dollars, the number of workers is between 45 and 55 . The operating budget varies from $ 8 , 000 to $ 12 , 000 per month. Let 10 , 000 x 0.7 y 0.3 = f ( x , y ) and the region is 45 ≤ x ≤ 55 and 8 ≤ y ≤ 12 , since y is represented in thousands of dollars. Thus, calculate ∬ R f ( x , y ) d x d y . Recall that the value of the integral ∬ R f ( x , y ) d x d y is ∫ a b ( ∫ c ( x ) d ( x ) f ( x , y ) d y ) d x where the region R is defined by a ≤ x ≤ b and c ( x ) ≤ y ≤ d ( x ) . Thus, ∬ R f ( x , y ) d x d y = ∫ 45 55 ( ∫ 8 12 10 , 000 x 0.7 y 0.3 d y ) d x . Simplify the integral ∫ 45 55 ( ∫ 8 12 10 , 000 x 0.7 y 0.3 d y ) d x with respect to y . ∫ 45 55 ( ∫ 8 12 10 , 000 x 0.7 y 0.3 d y ) d x = 10 , 000 ∫ 45 55 ( ∫ 8 12 x 0.7 y 0.3 d y ) d x = 10 , 000 ∫ 45 55 [ x 0.7 y 1.3 1.3 ] y = 8 12 d x = 10 , 000 ∫ 45 55 [ x 0.7 ( 12 1.7 1.3 − 8 1.7 1

WebAssign Printed Access Card for Waner/Costenoble's Applied Calculus, 7th Edition, Single-Term

7th Edition

ISBN: 9781337652742

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 8.5, Problem 42E

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To calculate: The average value of the number of gadgets the company can turn out per month where the productivity model at the company is P=10,000x0.7y0.3.

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WebAssign Printed Access Card for Waner/Costenoble's Applied Calculus, 7th Edition, Single-Term

Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 5-8, evaluate (a)...Ch. 8.1 - Prob. 6E Ch. 8.1 - For each function in Exercises 5-8, evaluate (a)...Ch. 8.1 - For each function in Exercises 5-8, evaluate (a)...Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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The average value of the number of gadgets the company can turn out per month where the productivity model at the company is P = 10 , 000 x 0.7 y 0.3 .

Solution Summary: The author calculates the average value of the number of gadgets a company can turn out per month based on the productivity model.

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To calculate: The average value of the number of gadgets the company can turn out per month where the productivity model at the company is P=10,000x0.7y0.3.

Chapter 8 Solutions