Question

The profits in hundreds of dollars, P(c), that a company can make from a product is modeled by a function of the price, c, they charge for the product: P(c) = –20c2 + 320c + 5,120. What is the maximum profit the company can make from the product?

Answer 1

The correct answer is B. 640,000

Explanation:

Answer 2

The maximum profit is the y-coordinate of the vertex of the parabola represented by the equation.


`P(c)=-20c^2+320c+5120 \\ \\ a=-20 \\ b=320 \\ \\ \hbox{the vertex } (h,k): \\ h=(-b)/(2a)=(-320)/(2 * (-20))=(-320)/(-40)=8 \\ k=f(h)=f(8)=-20 * 8^2+320 * 8+5120= \\ =-1280+2560+5120=6400`

The maximum value is 6400, but the profit is given in hundreds of dollars, so multiply the value by 100.

The maximum profit the company can make is $640,000.