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Math Help - need help with Maximization

  1. #1
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    need help with Maximization

    2. Suppose a company produces a commodity X using an input L. The production function is X =
    100L L2.
    (a.) Find what level of L maximizes production output, X.
    (b.) What levels of L generate an output of X = 0? (there are two different L values)
    (c.) Plot the production function
    (d.) Find the marginal product of labor (MPL).
    MPL=100-2L
    (e.) For what values of L is the MPL increasing and decreasing?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Jlittl23 View Post
    2. Suppose a company produces a commodity X using an input L. The production function is X =
    100L L2.
    (a.) Find what level of L maximizes production output, X.
    (b.) What levels of L generate an output of X = 0? (there are two different L values)
    (c.) Plot the production function
    (d.) Find the marginal product of labor (MPL).
    MPL=100-2L
    (e.) For what values of L is the MPL increasing and decreasing?
    Your production function is:

    X=100L - L^2

    Now as you have posted to the calculus forum you will have been taught that a maximum if one exists will be a root of:

     <br />
\frac{dX}{dL}=0 <br />

    So for part (a) you must differentiate X with respect to L set the derivative to zero and solve for L. Then you will need to check that this is indeed a maximum.

    CB
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