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?

Question

Mathematics

Sanaa Peck

24 May, 20:21

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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Answers (1)

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Brenna Carson · Answer 1

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