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22 October, 06:08

A certain company's main source of income is selling socks. The company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by: P (x) = - 3 (x-5) ^2+12. What sock price should the company set to earn a maximum profit?

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  1. 22 October, 06:16
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    For this case we have the following function:

    P (x) = - 3 (x-5) ^ 2 + 12

    We derive the function to obtain the maximum.

    We have then:

    P (x) = - 6 (x-5)

    We match zero:

    -6 (x-5) = 0

    We clear x:

    x-5 = 0

    x = 5

    Answer:

    the company should set a sock price of 5 $ to earn a maximum profit
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