Question

The profit in dollars in producing x items of some commodity is given by the equation P=−11x2+346.5x−2612.5.
How many items should be produced to break even?(If there are two break-even points, then enter the smaller value of x. Your solution may not be an integer. Use your calculator for irrational square roots.)



I know that P(x)=revenue - cost, but I don't know how to set revenue and cost equal to each other to find break-even if they are already combined in −11x2+346.5x−2612.5...

Answer 1

The function is P=−11x^2+346.5x−2612.5

Answer 2

break-even is where profit=0.

Answer 3

I think your equation already contains revenue and cost, since it is labeled as "profit"
I interpret "break-even" point as having no loss or profit, or , P = 0
so we want the roots of
-11x^2 + 346.5x - 2612.5

x = (-346.5 ± √(5112.25)/-22
= 12.5 or 19

Wolfram confirms my answers
http://www.wolframalpha.com/input/?i=−11x%5E2%2B346.5x−2612.5%3D0+

Answer 4

Oh yeah I forgot it meant that P = 0 thanks