A theater company's annual profit is modeled by the equation P= 0.2x^2-6.8x, where x is the number of plays performed in a year. How many plays must the company present in order to make a profit?

Answer 1

Solve P = 0 and take the positive of the two roots.

0.2x^2 -6.8x = 0
0.2x(x - 34) = 0

x = 34 plays produce break even.
35 productions (performances?) will produce a profit.

No wonder theaters go broke.