Question

The revenue in dollars generated from a sale of x picnic tables is given by R(x) = 41x - x²/500.

(a) Find the marginal revenue when 6000 tables are sold. To find the marginal revenue, start by finding the derivative of R(x) = 41x-x²/500
Find the marginal revenue when 6000 tables are sold.
(b) Estimate the revenue from the sale of the 6001st table by finding R'(6000).
C) The marginal revenue gives a ___ approximation of the actual revenue from the sale of the 6001st table because the marginal revenue is _____ the actual revenue.

Answer 1

To find the marginal revenue when 6000 tables are sold, find the derivative of the revenue function and evaluate it at x = 6000. To estimate the revenue from the 6001st table, substitute x = 6000 into the derivative. The marginal revenue gives an approximation of the actual revenue.

Step-by-step explanation:

(a) To find the marginal revenue, we need to first find the derivative of the revenue function, R(x) = 41x - x2/500. Taking the derivative, we get R'(x) = 41 - (x/250). To find the marginal revenue when 6000 tables are sold, substitute x = 6000 into R'(x) and evaluate.

(b) To estimate the revenue from the sale of the 6001st table, we need to find R'(x) where x = 6000. Substitute x = 6000 into R'(x) and evaluate.

(c) The marginal revenue gives an approximation of the actual revenue from the sale of the 6001st table because the marginal revenue is not equal to the actual revenue.