Calculus
posted by Anonymous .
"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!

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