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Math Help - Optimization Problem Help (Finding max value)

  1. #1
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    Optimization Problem Help (Finding max value)

    I am having some trouble on an optimization problem that I have for my homework assignment. It reads

    Assume that if the price of a certain book is p dollars, then it will sell x copies where x = 7000(1-p/35). Suppose the dollar cost of producing those x copies is 15000 + 2.5x. Finally assume that the company will not sell th book for more than $35. Determine the price of the book that will maximize profit.

    I know that revenue is equal to number of units sold multiplied by the price per unit.

    R = n x p

    I do not know how to approach the problem though. Should I start by solving for p in the equation x = 7000(1-p/35)?
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  2. #2
    Senior Member
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    Hi mate

    Quote Originally Posted by fishguts View Post
    I am having some trouble on an optimization problem that I have for my homework assignment. It reads

    Assume that if the price of a certain book is p dollars, then it will sell x copies where x = 7000(1-p/35). Suppose the dollar cost of producing those x copies is 15000 + 2.5x. Finally assume that the company will not sell th book for more than $35. Determine the price of the book that will maximize profit.

    the company sells 7000(1-p/35) books, but the cost of producing is 1500+2.5x, where x means the amount of sold books

    thus 1500+2.5*(7000)(1-p/35), because 7000(1-p/35) = x

    The company's costs are 1500+2.5*(7000)(1-p/35) depending on p, p = price

    The company sells 7000(1-p/35) books, gets p dollars for each sold book, that means it gets 7000(1-p/35)*p dollars

    Your profit now is Earned Dollars - Costs

    => f(p) = (7000*(1 - p/35))*p - 7000*(1 - p/35)

    You got to solve this:

    => f'(p) = ... (derive f)

    f''(p) = 0 => p = ...

    ---------

    i got p = $ 18
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