Question

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?

Answer 1

A quadratic function models the profit of the company and the maximum/minimum value of the quadratic function occurs on its vertex.

The given function is:


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

The equation is already in standard form, the vertex of the parabola as seen from the equation is (5,12)

This mean if the company sets the price of socks to $5 they will earn a maximum profit which is $ 12 million