Calculus Section 3.4 Calculate marginal cost, revenue, and profit

1. Calculus Section 3.4Calculate marginal cost, revenue, and profit If C(x) is the total cost of producing x units, then C’(x) is the marginal cost, the approximate cost of producing the x+1 (next) unit. If R(x) is the total revenue from selling x units, then R’(x) is the marginal revenue, the approximate revenue from the sale of the x+1 (next) unit. If P(x) is the total profit from producing and selling x units, then P’(x) is the marginal profit, the approximate profit from producing and selling the x+1 (next) unit.

2. Notation MC(x) = C’(x) Marginal Cost MR(x) = R’(x) Marginal Revenue MP(x) = P’(x) Marginal Profit

3. example The cost of the production of x textbooks is C(x) = 140 + 10x - .02x2, the revenue is R(x) = 95x - .01x2. Find the following. • The cost of producing 100 textbooks • The marginal cost • The approximate cost of the 101st textbook • The marginal revenue • The approximate revenue from the 101st textbook • The marginal profit • The approximate profit from the 101st textbook

4. Example A potato chip maker says that the company’s profit on the manufacture and sale of x, 8-ounce bags of chips (0 ≤ x ≤ 500) is given by P(x)=.0005x2 + x - 160 dollars. a. Determine the total profit on 200 bags. b. How much will the company lose if it makes and sells only 50 bags? c. Find the marginal profit function. d. Find the profit generated by the 201st bag.

5. assignment page 136 problems 2 – 42 even page 138 problem 1