The total profit function P(x) for a company producing x thousand units is given by P(x) = -3x^2 + 36x - 81. How do you find the values of x for which the company makes a profit?

1 Answer
Jul 24, 2015

I found: 3<x<9 (in thousand units)

Explanation:

You can try plotting your function considering that it represents a parabola:
enter image source here

You can see that producing zero units (x=0, i.e., the company is idle) you get a loss, P(0)=-81 this is because you have to pay fixed costs, say, taxes, rent...etc.
There is a region where P(x)>0 and you have a profit, where:
-3x^2+36x-81>0 that gives you (using the Quadratic Formula):
3<x<9 (in thousand units) that described the red shaded region int the graph where P(x)>0.