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Math Help - Optimal production?

  1. #1
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    Optimal production?

    I need to find the optimal level of inputs, the minimum total cost, and the average cost given the following conditions:

    Min 25K + 5L
    s.t. 100=L^{.75}K^{.25}

    The second equation looks like a standard Cobb-Douglas production function, but I don't understand how they interact.
    Last edited by Quixotic; October 1st 2010 at 06:18 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Quixotic View Post
    I need to find the optimal level of inputs, the minimum total cost, and the average cost given the following conditions:

    Min 25K + 5L
    s.t. 100=L^{.75}K^{.25}

    The second equation looks like a standard Cobb-Douglas production function, but I don't understand how they interact.
    The constraint condition is:

    100=L^{3/4}K^{4}

    raise this to the fourth power:

    10^8=L^3K

    so

    K=\dfrac{10^8}{L^3}

    Substituting this into the objective gives:

    Ob(L)=\dfrac{25 \times 10^8}{L^3}+5L

    Now the minimum of the objective occurs when:

    \dfrac{d}{dL}Ob(L)=0

    etc.

    CB
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