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Math Help - Finding minimum of average cost

  1. #1
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    Post Finding minimum of average cost

    A company has found that the total cost T(q) $ for product of q boxes can be calculated as:
    T(q)=0.01q^2-2q+5000 , q>0
    How many box has to be produced to the average cost of A(q)=T(q)/q become as low as possible?

    Thanks for your help.
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  2. #2
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    A(q) = T(q)/q = 0.01q - 2 + 5000/q

    Now use what you know from calculus to minimize this (take derivative, set it to equal to 0, ...)
    Also, q needs to be a natural number, so make sure to take this into account.

    As a side note, what company pays $5000 for 0 boxes? [edit: never mind, q > 0]
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  3. #3
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    A(q) = T(q)/q = 0.01q + 5000/q - 2


    as A(q) is minimum, 0.01q=5000/q

    q=500sqrt(2)

    q=707(approx.)
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