Some antiderivatives and itengrals. A coffee company has found that the marginal

Question

Some antiderivatives and itengrals.

A coffee company has found that the marginal cost, in dollars per pound, of the coffee it roasts is represented by the function below, where x is the number of pounds of coffee roasted. Find the total cost of roasting 470 lb of coffee, disregarding any fixed costs. C'(x) = -0.013x+ 8.25. for x 600 The total cost is . A note card company has found that the marginal cost per card of producing x note cards is given by the function below, where C'(x) is the marginal cost, in cents, per card. Find the total cost of producing 690 cards, disregarding any fixed costs. C'(x) = -0.08x+ 80, for x 1000 The total cost is cents A concert promoter sells tickets and has a marginal-profit function given below, where P'(x) is in dollars per ticket. This means that the rate of change of total profit with respect to the number of tickets sold. x. is P'(x). Find the total profit from the sale of the first 160 tickets, disregarding any fixed costs. P'(x) =4x - 1104 The total profit is . (Round to the nearest cent as needed.) A clothing company determines that its marginal cost, in dollars per dress, is given by the function below. Find the total cost of producing the first 190 dresses, disregarding any fixed costs. The total cost is . (Round to the nearest cent as needed.) Some antiderivatives and itengrals.

Explanation / Answer

1.

C(x) = -0.013/2 * x^2 + 8.25 *x At x = 470 is

C(470) = 2441.65

2.

C(x) = -0.04*x^2 + 80*x

C(690) = 36156

3.

P(x) = -2x^2 + 1104x

C(160) = 125440

4.

C(x) = -(1/25)*x^2 + 56*x

C(x) = 9196

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