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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

A manager estimates that if the company charges p dollars for their new product, where 0 less than or equal to p less than or equal to 200, then the revenue from the product will be function r of p = 2000*p-(10*p^2) dollars each week. According to this model, for which of the following values of p would the company’s weekly revenue for the product be the greatest?

(A) 10
(B) 20
(C) 50
(D) 100
(E) 200

答案和解析

答案：D

解析：

The graph of function r of (p) = 2000*p-(10*p^2) is a downward-facing parabola that intersects the x-axis at 0 and at 200. Parabolas are symmetric, so the maximum value of r occurs at 100, which is halfway between 0 and 200. (When p=100, the value of r is function r of 100=(2000*(100))-(10*(100^2))=100000.)