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Math Help - maximizing profit

  1. #1
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    Smile maximizing profit

    Use calculus to find the production level x that will maximize profit if the price (also known as demand) is p(x)=12-(x/500) and the cost is C(x)=680+4x+0.01x^2

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  2. #2
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    Quote Originally Posted by xSMUxCHEERLEADINGx View Post
    Use calculus to find the production level x that will maximize profit if the price (also known as demand) is p(x)=12-(x/500) and the cost is C(x)=680+4x+0.01x^2

    {\rm{Profit}=Revenue-Costs}=xp(x)-C(x)=12x-\frac{x^2}{500}-680-4x-0.01x^2 =-0.012x^2+8x-640

    So to find the production that maximises profit we differentiate the quadratic on the right above and set the derivative to zero and solve for x.

    CB
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