Calculus

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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!

  • Calculus -

    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

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