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Math Help - cost function.

  1. #1
    Junior Member
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    cost function.

    For the given cost function
    C(x)=52900+200x+x2 find:
    a) The cost at the production level 1000 = $1252900
    b) The average cost at the production level 1000 = $1252.9
    c) The marginal cost at the production level 1000 = $2201

    d) The production level that will minimize the average cost?
    e) The minimal average cost?

    I know you have to divide c(x) by x units, then take the derivative... but it's just not working out for me.
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by B-lap View Post
    For the given cost function
    C(x)=52900+200x+x2 find:
    a) The cost at the production level 1000 = $1252900
    b) The average cost at the production level 1000 = $1252.9
    c) The marginal cost at the production level 1000 = $2201

    d) The production level that will minimize the average cost?
    e) The minimal average cost?

    I know you have to divide c(x) by x units, then take the derivative... but it's just not working out for me.
    A(x) = \frac{52900+200x+x^2}{x}=\frac{52900}{x}+200+x

    A'(x) = \frac{-52900}{x^2} + 1

    Find the critical number by setting it equal to zero, since it cannot be undefined; well, it can, but you get x=0 which makes no sense.

    x^2 = 52900

    so x=230

    You may want to justify that it's a min (and not a max!) using one of the derivative tests.

    The attached summary I give out to my students might help. Good luck!!
    Attached Files Attached Files
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