If a company has total costs C(x) = 20,000 + 25x + 0.2x2 and total revenues given by R(x) = 475x − 0.8x2, find the break-even points.

Answer 1

break-even where R=C, so just solve

20,000 + 25x + 0.2x^2 = 475x − 0.8x^2

Rearrange and collect terms, and then just use the quadratic formula.