The function f of x is equal to negative open paren x minus 20 close paren times open paren x minus 100 close paren 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 quadratic because its leading coefficient is negative, so its greatest value occurs at the vertex. Its zeros are x = 20 and x = 100, so the vertex lies halfway between them: (20 + 100) / 2 = 60. Therefore, 60 purchase orders will generate the greatest profit, which is choice B.

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