A company's profit function is given by P(x) = -x^3 + 6x^2 + 15x - 20, where x is the number of thousands of units produced. What is the marginal profit when 3,000 units are produced?

Core Concept

Marginal profit is the derivative of the profit function. First, find P'(x) = -3x^2 + 12x + 15. When x = 3 (since we're producing 3,000 units), P'(3) = -3(3)^2 + 12(3) + 15 = -27 + 36 + 15 = 24. Since x is in thousands of units, the marginal profit is $24,000 per thousand units, which is $6,000 per unit. Therefore, the correct answer is A) $6,000 per thousand units.