If the marginal revenue (in dollars per unit) for a month is given by MR = –0.4x + 250, what is the total revenue from the production and sale of 50units?
If the marginal revenue (in dollars per unit) for a month is given by MR = –0.4x + 250, what is the total revenue from the production and sale of 50units?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![### Calculating Total Revenue from Marginal Revenue
If the marginal revenue (MR) in dollars per unit for a month is given by the equation:
\[ MR = -0.4x + 250 \]
where \( x \) represents the number of units, determine the total revenue from the production and sale of 50 units.
To find the total revenue, integrate the marginal revenue function with respect to \( x \) from 0 to 50:
\[ \text{Total Revenue} = \int_{0}^{50} (-0.4x + 250) \, dx \]
Apply the integral:
\[
\int (-0.4x + 250) \, dx = -0.2x^2 + 250x + C
\]
Evaluate from 0 to 50:
\[
\text{Total Revenue} = \left[-0.2(50)^2 + 250(50)\right] - \left[-0.2(0)^2 + 250(0)\right]
\]
Calculate the values:
\[
= \left[-0.2(2500) + 12500\right] - [0]
\]
\[
= (-500 + 12500)
\]
\[
= 12000
\]
Thus, the total revenue from the production and sale of 50 units is $12,000.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21aa43ce-550d-41c6-9c29-d391c001c38a%2F0e7d87eb-d216-4f98-99ba-31fad20c84a0%2Fkkrq07b_processed.png&w=3840&q=75)
Transcribed Image Text:### Calculating Total Revenue from Marginal Revenue
If the marginal revenue (MR) in dollars per unit for a month is given by the equation:
\[ MR = -0.4x + 250 \]
where \( x \) represents the number of units, determine the total revenue from the production and sale of 50 units.
To find the total revenue, integrate the marginal revenue function with respect to \( x \) from 0 to 50:
\[ \text{Total Revenue} = \int_{0}^{50} (-0.4x + 250) \, dx \]
Apply the integral:
\[
\int (-0.4x + 250) \, dx = -0.2x^2 + 250x + C
\]
Evaluate from 0 to 50:
\[
\text{Total Revenue} = \left[-0.2(50)^2 + 250(50)\right] - \left[-0.2(0)^2 + 250(0)\right]
\]
Calculate the values:
\[
= \left[-0.2(2500) + 12500\right] - [0]
\]
\[
= (-500 + 12500)
\]
\[
= 12000
\]
Thus, the total revenue from the production and sale of 50 units is $12,000.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning