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

Answer:

The correct answer is B. 640,000

Step-by-step explanation:

Answer 2

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

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

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.