Expert: Scott A Wilson - 11/21/2011

Question
Your company would like to know how sales levels affect profits. If too few items are sold, then there is a loss. Even if too many items are sold, however, the company can lose money (likely because of low pricing). It is good to know how many items can be sold for there to be profit.

The following function expresses profit in terms of the number of phones sold by a particular company:

P(x) = –x2 + 110x – 1,000

This function can be used to compute the profit (in thousands of dollars) from producing and selling a certain number, x, of thousands of smartphones.

a.Compute the following: P(5), P(50), and P(120). Then, interpret the results.

Answer
It is known that P(x) = –x^2 + 110x – 1,000.

Given this, it can be said that P(5) = -25 + 550 - 1,000 = -475,
P(50) = -2,500 + 5,500 - 1,000 = 2,000, and
P(120) = -14,400 + 13,200 - 1,000 = -2,200.

This means that if too many or too few of the items are sold, the profit would really be a loss since it is negative at high and low values.