SOLUTION: The total profit function P(x) for a company producing x thousands of pens is given by P(x) = -2x2 + 26x + 44. Find the values of x for which the company makes a profit. [Hint: T

Algebra ->  Graphs -> SOLUTION: The total profit function P(x) for a company producing x thousands of pens is given by P(x) = -2x2 + 26x + 44. Find the values of x for which the company makes a profit. [Hint: T      Log On


   

Question 1187664: The total profit function P(x) for a company producing x thousands of pens is
given by P(x) = -2x2 + 26x + 44. Find the values of x for which the company makes a profit. [Hint: The company makes a profit when P(x) > 0].
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
P%28x%29+=+-2x%5E2+%2B+26x+%2B+44
The company makes a profit when P%28x%29+%3E+0
-2x%5E2+%2B+26x+%2B+44%3E+0...........simplify
-x%5E2+%2B+13x+%2B+22%3E+0
using quadratic formula we get:+x=%281%2F2%29+%2813+-+sqrt%28257%29%29 or+x=%281%2F2%29+%2813+%2B+sqrt%28257%29%29
so, P%28x%29+%3E+0 if
%281%2F2%29+%2813+-+sqrt%28257%29%29%3C+x%3C+%281%2F2%29+%2813+%2B+sqrt%28257%29%29........exact solution
approximately
-1.5%3C+x%3C+14.5+
disregard negative value since P%28x%29+%3E+0
The company makes a profit when 0%3C+x%3C+14.5+

graph%28300%2C300%2C-10%2C20%2C-20%2C200%2C-2x%5E2%2B26x%2B44%29


Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.

To answer the question, solve this quadratic equation

            -2x^2 + 26x + 44 = 0.

and find its real roots.


The domain you are looking for is the set of positive real numbers between the roots.