Expert: Sherman D. - 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
this is quit easy to explain. Since x^2 is negative, you get a graph with a maximum. Anything above x = 0 value, is considered profit. If you go to www.calculator.com, click on graphing, then type in -(x^2) + 120x - 2000, you will get the x-intercepts 20 and 100, and if you notice everything between 20 and 100 is above x = 0, and therefore at those values between 20 and 100 is considered profit, so your answer would be 20 < x < 100.

You can also use the formula
x = (-b ± sqrt(b^2 - 4ac))/2a
whereas
a = -1
b = 120
c = -2000

you can also use
x = -b/(2a)
to find the price of each cold sold, which will give you the maximum profit that was made, by substituting the value you get for x into your problem.