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Math Help - Need help

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    7

    Need help

    A manufacturuer can produce radios at a cost of $5 apiece. The radios have been selling for $9 apiece, and at this price, consumers have been buying 6,000 radios a month. The manufacturer is planning to raise the price of radios and estimates that for each $1 increase in price, 300 fewer radios will be sold a month. What should be the selling price in order to maximize profit?

    Need step by step help solving this problem.
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  2. #2
    Newbie
    Joined
    Aug 2007
    Posts
    23
    Here are some steps you could try.

    1. Find the function relating price to quantity sold.
    ie. f(price)=quantity

    2. Find the functions for gross profit and costs in terms of the above function.
    ie. f(price)=gross and f(price)=costs

    3. Subtract to get the net profit function.
    ie. f(price)=net

    4. Differentiate to find the maximum
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