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Math Help - Max min problem involving maximum profit (Math 113)

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    Max min problem involving maximum profit (Math 113)

    I really can't seem to solve this question and have tried mulitple ways of doing this, so here's hoping some one can help me or give me hints.

    It cost 14 dollars to manufacture a backpack. If the backpack sells at x dollars each, the number sold, n, is given by n = (7/(x-4)) +5(100-x). What selling price would maximize profit?

    I can't seem to get critical point and the question says to "simplify" implying that my answer should be an exact value.
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    Quote Originally Posted by KatherineJK View Post
    I really can't seem to solve this question and have tried mulitple ways of doing this, so here's hoping some one can help me or give me hints.

    It cost 14 dollars to manufacture a backpack. If the backpack sells at x dollars each, the number sold, n, is given by n = (7/(x-4)) +5(100-x). What selling price would maximize profit?

    I can't seem to get critical point and the question says to "simplify" implying that my answer should be an exact value.
    Note that profit = n(x - 14):

    P = \left(\frac{7}{x - 4} + 5 (100 - x)\right) (x - 14) = 7 + 5 (100 - x)(x - 14).

    You should be able to find the maximum turning point of this function.
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