Set R(x) equal to C(x). Solve the resulting equation for x, paying attention to the domain of C(x):
Solve 200x-2x^2 = -x^2 + 25x + 31000 for x greater than or equal to zero but less than or equal to x. That means you must reject any solution outside of this domain.
Rearrange all of these terms on the left side of your equation and place zero on the right side. Next, rearrange all of the terms on the left side in descending order by powers of x. Next, solve the resulting quadratic equation. Make certain to reject any x that does not fall within [0,100].
