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Math Help - Maximum Profit

  1. #1
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    Maximum Profit

    The demand for a certain product is given by the model p=53/sqrt(x). the fixed costs are $608 and the cost per unit is $0.53. Find the production level x that yields the maximum profit if x is between [0,7530]

    I know that P=R-C and thats about it
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  2. #2
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    After thinking about this I tried to do it, can somebody please check my work

    P=R-C
    R=xp C=0.53x+608
    R=53x/sqrt(x)

    P=53x/sqrtx-0.53x-608
    P=53sqrt(x)-0.53x-608
    DP/dx=53/2sqrt(x)-0.53
    0=53/sqrt(x)-0.53
    x=2500


    Please Help
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