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Math Help - Solving rational inequalties application problem help

  1. #1
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    Solving rational inequalties application problem help

    Here's the problem:

    An economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. These functions are R(x)=-x^2+10x and C(x)=4x+5, respectively, where x is the number of snowboards produced, in thousands. The average profit is defined by the function AP(x) = P(x) / x , where P(x) is the profit function. Determine the production levels that make AP(x) > 0

    What i did is :

    -x^2+1x   +  4x+5   >  0


    Is this the right inequality to solve the problem?
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  2. #2
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    Won't profit be \displaystyle P(x) = R(x)-C(x) = -x^2+10x-(4x+5) = -x^2+6x-5 ?
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  3. #3
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    Quote Originally Posted by pickslides View Post
    Won't profit be \displaystyle P(x) = R(x)-C(x) = -x^2+10x-(4x+5) = -x^2+6x-5 ?
    Yeh, so i factored out the negative and put the equation into the quadratic formula to find the x's which are 6.74 and -0.74. So -0.74 < x < 6.74

    but the answer according to the book is 1 < x < 5
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