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Math Help - minimizing cost

  1. #1
    413
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    minimizing cost

    Suppose that a cost-minimizing firm's production function is given to be
    Q = (20)*(M^0.5)*(W^0.5)
    where M stands for the labor of men and W stands for the labor of women (Both of which are expressed in person-hours).
    Suppose men receive $6 per hour and women receive $5.50 per hour. Moreover, suppose the firm uses 400 person-hours of W and 625 person-hours of M to produce 10,000 units of output.
    Is this firm minimizing the cost of producing this given level of output? If not, explain what this firm should do?


    How should i approach this question?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by 413 View Post
    Suppose that a cost-minimizing firm's production function is given to be
    Q = (20)*(M^0.5)*(W^0.5)
    where M stands for the labor of men and W stands for the labor of women (Both of which are expressed in person-hours).
    Suppose men receive $6 per hour and women receive $5.50 per hour. Moreover, suppose the firm uses 400 person-hours of W and 625 person-hours of M to produce 10,000 units of output.
    Is this firm minimizing the cost of producing this given level of output? If not, explain what this firm should do?


    How should i approach this question?
    First the question needs some clarification.

    M is the number of hours of man labour employed
    W the number of hours of woman labour employed.

    Production is Q, and that requires:

    M=(Q/10000)625 ... (1)
    W=(Q/10000)400 ... (2)

    Cost:

    C(Q)=6M + 5.5W ... (3)

    Now the question appears to be:

    Does Q = (20)*(M^0.5)*(W^0.5) minimise (3) subject to (1) and (2)?

    I'm not sure that this makes any sense!

    RonL
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