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

Answer:

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#.