Posted by Anonymous on Monday, April 4, 2011 at 9:53am.
"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  bobpursley, Monday, April 4, 2011 at 11:19am
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 This Question
Related Questions
 Calculus  "The production amount, Q, of an item manufactured by a company is ...
 Economics  Consider the following simplified economy described by a Cobb...
 Macroeconomics help!  Consider the following simplified economy described by a ...
 Microeconomics: Cost of Production  Please help me with this question! QUESTION...
 Economy  How to draw isoquant curves for a certain quantity? What does "...
 Economics  The chapter is on Production and costs in thelong run, we are given ...
 Microeconomics  Suppose that the market labor supply and labor demand equations...
 calculus  Rice production requires both labor and capital investments in ...
 lavin  A firm has the following shortrun production function: Q = 100L + 10L2...
 ECONOMICS  1) If the price of a product produced in a competitive market ...
More Related Questions