Maximizing profit help?

Question

If C(x) = 18000 + 500x − 1.2x² + 0.004x³ is the cost function and p(x) = 2900 − 6x is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)

Answer 1

Profit = R - C = x(2900 - 6x) - (18000 + 500x - 1.2x² + .004x³

Note: Maximizing P by taking dP/dx = 0 is the same as saying dR/dx = dC/dx

Here dP/dx = 2900 - 12x - 500 + 2.4x - .012x² = -.012x² - 9.6x + 2400

You can now use quadratic formula to solve for x.

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