Expert: Bobby Soltani - 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 profit in this case is like the y variable when you normally graph a curve.  The question wants you to find what values of x will make P a positive number.  For instance, x = 0, P = -2000, so this would not be in the range of x's.  Since the x^2 term is negative, we know it is a parabola that opens downward.  Use the quadratic formula to solve for the zeros of the function.  Or, if you realize that it can be factored, the zeros are easily found:
P(x) = -x^2-120x+2000 = (-x+100)(x-20)

This gives zeros at x = 20 and x = 100.  Since we know it is a parabola that opens downward, we know that P is greater than zero from 20 < x < 100.

Let me know if you have questions.

Bobby