Your automobile assembly plant has a Cobb-Douglas production function given by q = x0.4,0.6, where q is the number of automobiles it produces per year, x is the number of employees, and y is the daily operating budget (in dollars). Annual operating costs amount to an average of $23,000 per employee plus the operating budget of $365y. Assume that you wish to produce 5,000 automobiles per year at a minimum cost. How many employees should you hire? (Round your answer to the nearest employee.) X= employees

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.8: Joint And Combined Variation
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Your automobile assembly plant has a Cobb-Douglas production function given by
9 = x0.4 0.6
where q is the number of automobiles it produces per year, x is the number of employees, and y is the daily operating budget (in dollars). Annual operating costs amount to an average of $23,000 per
employee plus the operating budget of $365y. Assume that you wish to produce 5,000 automobiles per year at a minimum cost. How many employees should you hire? (Round your answer to the
nearest employee.)
X=
employees
Transcribed Image Text:Your automobile assembly plant has a Cobb-Douglas production function given by 9 = x0.4 0.6 where q is the number of automobiles it produces per year, x is the number of employees, and y is the daily operating budget (in dollars). Annual operating costs amount to an average of $23,000 per employee plus the operating budget of $365y. Assume that you wish to produce 5,000 automobiles per year at a minimum cost. How many employees should you hire? (Round your answer to the nearest employee.) X= employees
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