Maximize Profit: Find Optimal Production with C(x) & R(x)

[antinerd]

Homework Statement

Find the level of production x that will maximize profit.

Homework Equations

C(x) = 500 + 100x^2 + x^3, where x = units produced.

R(x) = 7000x - 80x^2

The Attempt at a Solution

Should I use marginal cost and marginal revenue, or is there a way to just use the equations directly to find the profit maximization?

 

[EnumaElish]

Profit = R - C. x* maximizes Profit if Profit'(x*) = 0 and Profit"(x*) < 0.

If you think about it it should be clear that MR = MC amounts to the same first order condition as above.