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?

Because the quadratic opens downward, its maximum occurs at the vertex. The price at the vertex is c = −320 ÷ (2 × −20) = 8. Substituting gives P(8) = −20(8²) + 320(8) + 5,120 = 6,400 hundreds of dollars, or $640,000. The maximum profit is $640,000, choice B.

AI-written and checked against the verified answer.