Question

If the total revenue received from the sale of x items is given by R(x) = 40ln(3x+1), while the total cost to produce x items is C(x) = x/3, find the following: (a) The marginal revenue (b) The profit function P(x) (c) The marginal profit when x = 120 (d) Interpret the results of part (c).

Name: if total revenue received from the sale of x items is given by rx 40ln3x1 while the total cost to produce x items is cxx3 find the following a the marginal revenue b the profit function px c 81096
Uploaded: 2022-02-16T00:54:26-08:00
Duration: 3 min
Channel: Suman Saurav Thakur
Description: if total revenue received from the sale of x items is given by rx 40ln3x1 while the total cost to produce x items is cxx3 find the following a the marginal revenue b the profit function px c 81096

          If the total revenue received from the sale of x items is given by R(x) = 40ln(3x+1), while the total cost to produce x items is C(x) = x/3, find the following:
(a) The marginal revenue
(b) The profit function P(x)
(c) The marginal profit when x = 120
(d) Interpret the results of part (c).

Added by Gregory T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Suman Saurav Thakur

02/16/2022

Step 1

Given: \(R(x) = 40\ln(3x+1)\) To find the marginal revenue, we need to differentiate the revenue function with respect to x. \[MR(x) = \frac{dR}{dx} = \frac{d}{dx}(40\ln(3x+1))\] \[MR(x) = 40 \cdot \frac{1}{3x+1} \cdot 3 = \frac{120}{3x+1}\] Show more…

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If the total revenue received from the sale of x items is given by R(x) = 40ln(3x+1), while the total cost to produce x items is C(x) = x/3, find the following: (a) The marginal revenue (b) The profit function P(x) (c) The marginal profit when x = 120 (d) Interpret the results of part (c).