Question

Revenue, cost, and profit. The price-demand equation and the cost function for the production of table saws are given, respectively, by x = 6,000 - 30p and C(x) = 72,000 + 60x where x is the number of saws that can be sold at a price of $p per saw and C(x) is the total cost (in dollars) of producing x saws.

(A) Express the price p as a function of the demand x, and find the domain of this function.
(B) Find the marginal cost.

Answer 1

To express the price p as a function of the demand x, we can substitute the given demand equation into the price-demand equation. The domain of this function is x ≥ 0. The marginal cost is a constant value of 60.

Step-by-step explanation:

To express the price p as a function of the demand x, we can substitute the given demand equation into the price-demand equation: x = 6,000 - 30p. Solving for p, we get p = (6,000 - x)/30. The domain of this function is the set of all possible values of x that make the price nonnegative, so the domain is x ≥ 0.

The marginal cost is the derivative of the cost function with respect to the quantity x. Taking the derivative of C(x) = 72,000 + 60x, we get C'(x) = 60. Therefore, the marginal cost is a constant value of 60.