The function f(x) = –(x – 20)(x – 100) represents a company’s monthly profit as a function of x, the number of purchase orders received. Which number of purchase orders will generate the greatest profit?

The profit function is a downward-opening parabola because its leading coefficient is negative, so its greatest value occurs at the vertex. Its zeros are 20 and 100, so the vertex lies halfway between them: (20 + 100) ÷ 2 = 60. Therefore, 60 purchase orders generate the greatest profit.

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