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