Expert: Ahmed Salami - 1/9/2005

Question
The profit a coat manufacturer makes each day is modeled by the equation P(x)=-x^2+120x-2000, where P is the profit and x is the price for each coat sold.For what values of x does the company make a profit?
I don \'t understand this problem(how to do it) and hope you can help me.However, the answer key says that the answer is 20<x<100. Thanks.

Answer
Hi Jeff,
The company make a profit when P > 0 i.e
-x^2 + 120x - 2000 > 0
multiplying both sides by -1 and therefore changing the sign gives
x^2 - 120x + 2000 < 0
(x-100)(x-20)< 0
The nature of this graph shows that this will happen for
20 < x < 100
You can always get back to me on it.
Regards.