Quandaries
and Queries 

The profit a coat manufacturer makes each day is modeled by the equation P(x)=x^{2}+120x2000, 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. 

Hi Abraham, The function gives the "profit" of the manufacturer as a function of x, the number of coats sold. For some values of x this function is negative, in particular if x = 1 then p(1) is negative. We usually think of profit being positive, a manufactuter is not going to survive if they don't made a (positive) profit. The question is asking "For what values of x is P(x) positive?" Penny 

