An electronics store is selling personal CD players. The regular price for each
CD player is $90. During a typical two weeks, the store sells 50 units. Past
sales indicate that for every $1 decrease in price, the store sells five more
units during two weeks. Calculate the price that will maximize revenue

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  1. revenue = price * units

    x = the price decrease

    r = (90 - x) (50 + 5x) = 4500 + 400 x - 5 x^2

    the max is on the axis of symmetry ... where the 1st derivative equals zero

    dr/dx = 400 - 10 x

    400 - 10 x = 0 ... x = 40

    price for max revenue = 90 - 40

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