R(x) = – 0.01x2 + 2x + 2000, and the cost is C(x) = 0.08x + 1000. Find the marginal revenue, marginal cost, and marginal profit for a production after 55 units.

Answer 1

Marginal cost = C'(x) = 0.08

Marginal revenue = R'(x) = -.02x + 2

Marginal Profit = R'(x) - C'(x) = -.02x + 2 - .08 = -.02x + 1.92

At x = 55, marginal cost equals .08, marginal revenue -.02(55) + 2 = .9, marginal profit = -.02(55) + 1.92 = .82