Explanation Given information: The production function for the company is given by P = f ( N , V ) = 5 N 0.75 V 0.25 Where Pis the company production output, N is the number of workers; V is the value of the equipment, in units of $25,000. The employs 80 workers and has equipment worth $750,000. Calculation: The employs 80 workers and has equipment worth $750,000. ⇒ N = 80 ; V = 750 , 000 25 , 000 = 30 u n i t s Therefore, N = 80 and V = 30 units P = f ( N , V ) = 5 N 0.75 V 0.25 (Given) Differentiating P with respect to ‘N’, we get f N ( N , V ) = 5 ( 0.75 ) N 0.75 − 1 V 0.25 = 3.75 N − 0.25 V 0.25 Differentiating P with respect to ‘V’, we get f V ( N , V ) = 5 ( 0.25 ) N 0.75 V 0.25 − 1 = 1.25 N 0.75 V − 0.75 Therefore, f ( 80 , 30 ) = 5 ( 80 ) 0.75 ( 30 ) 0.25 = 5 ( 26.75 ) ( 2.34 ) ≈ 313 t o n s f N ( 80 , 30 ) = 3

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Chapter 8.4, Problem 25P

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The value of N and V, the values of f,fN,fV at these values of N and V, and its units andexplain the meaning of each value in terms of production.

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Chapter 8.4, Problem 24P

Chapter 8.4, Problem 26P

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The value of N and V, the values of f , f N , f V at these values of N and V, and its units andexplain the meaning of each value in terms of production.

Solution Summary: The author explains the meaning of N and V in terms of production. The company employs 80 workers and has equipment worth 750,000.

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To find:

The value of N and V, the values of f,fN,fV at these values of N and V, and its units andexplain the meaning of each value in terms of production.

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Chapter 8 Solutions

The value of N and V, the values of f , f N , f V at these values of N and V, and its units andexplain the meaning of each value in terms of production.

Solution Summary: The author explains the meaning of N and V in terms of production. The company employs 80 workers and has equipment worth 750,000.

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To find: The value of N and V, the values of f,fN,fV at these values of N and V, and its units andexplain the meaning of each value in terms of production.

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Chapter 8 Solutions

To find:

The value of N and V, the values of f,fN,fV at these values of N and V, and its units andexplain the meaning of each value in terms of production.