The profit from a business is described by the function P(x) = –4x^2 + 16x + 25, where x is the number of items made, in thousands, and P(x) is the profit in dollars.

Question

How many items will maximize the profit?

Here are the answer choice:

A. 1,000

B. 2,000

C. 3,000

D. 4,000

Answer 1

To find the max value, you are looking for the vertex of this parabola. You can do this using the following formula:

x=-b/(2a)

x=-16/(2*-4)

x=-16/-8

x=2

Since this is in thousands,

B. 2,000