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?
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
