Find the marginal cost, marginal revenue, and marginal profit functions. Find all values of x for which the marginal profit is zero.

C (x) = 5x

R (x) = 8x - 0.001x^2

Let P (x) be the profit function and is equivalent to the difference of revenue and cost.

P (x) = R (x) - C (x)

P (x) = 8x - 0.001x² - 5x

P (x) = 3x - 0.001x²

Profit is 0 so:

0 = 3x - 0.001x²

x = 0, x = 3000

The profit is 0 when x is 0 or 3000.