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"The quantity, q, of a product manufactured depends on the number of workers, W, and the amount of capital invested, K, and is given by

q = 6 * W^(3/4) * K^(1/4)

Labor costs are $10 per worker and capital costs are $20 per unit, and the budget is $2000.

What are the optimum number of workers and the optimum number of units of capital?"

Thank you in advance for any help!

Question ID
525205

Created
April 4, 2011 1:53pm UTC

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0

URL
https://questions.llc/questions/525205

Answers
2

Views
936

2 answers

  1. 2000=(q)(10+20)

    q=2000/30=667

    dq=6*3/4*w^-.25 K^.25 + 6w^.75 * .25K^-.75 =0

    18/4*K=6/4 w
    3K=w

    but from the original equation
    667=6 w^.75 * (w/3)^.25
    667=6 w (1/3)^.25

    and you have w, then go back and k is 3 times that.

    check my work, it is easy to err when typing these

    Answer ID
    525237

    Created
    April 4, 2011 3:19pm UTC

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    0

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  2. 12

    Answer ID
    1656051

    Created
    December 5, 2017 6:24am UTC

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