The profit from a business is described by the function P(x) = −4xto the power of 2 + 16x + 25, where x is the

Question

The profit from a business is described by the function P(x) = −4xto the power of 2 + 16x + 25, where x is the number of items made, in thousands, and P(x) is the profit in dollars. How many items will maximize the profit? A.	1000 B.	2000 C.	3000 D.	4000

GPT-5 mini · Answer

P(x) = −4x^2 + 16x + 25 is a downward parabola. The vertex (maximum) occurs at x = −b/(2a) = −16/(2·(−4)) = 2.

Since x is in thousands, 2 corresponds to 2000 items. Answer: B.

The profit from a business is described by the function P(x) = −4xto the power of 2 + 16x + 25, where x is the number of items made, in thousands, and P(x) is the profit in dollars. How many items will maximize the profit? A. 1000 B. 2000 C. 3000 D. 4000

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