After some market research, an online music service has estimated that the numbe

Question

After some market research, an online music service has estimated that the number of music files, in thousands, that they can expect to sell annually if the files are priced at p dollars each is approximately f(p) = 142 ? 91.1 p . (a) Write an equation for the annual revenue the service can expect when the files are p dollars each. R(p) = thousand dollars (b) Use a graphing calculator to estimate the price at which the annual revenue is maximized. (Round your answer to two decimal places.) p = $ How many music files will be sold at this price? (Round your answer to three decimal places.) thousand

Explanation / Answer

A) Revenue = Quantity x price = f(p) x p = (142 -91.1p)pv=142p - 91.1p^2 =R(p) b) dR(p)/dp =0 = 142 -182.2 p = 0 so p = $ 0.779 c)f(p) = 142 -91.1 p = 71 thousand

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