Yaster Outhers manutachures and welh estreme-cold sleeping bags The table below shows the price-demand and total cost data where Revenue Model ph the wholesale price in dollan of a sleeping bag for a weekly demand ofsleeping bags Cisthe total cost n dullard of producing sleeping bags Using the regression model computed above, find a model for the weekly revenue, using z as the a sleeping bags independent variable. 1240 13.000 NOTE: Do not calculate another regression Use the price equation to find a model for revenue R(2) -p-a. 20 235 14300 180 155 18.500 R(z)-p-z (a + bz + cz)a ar + ba+e 1220 s0 21.000 Cost Model Find a linear regression model for the weekly cost data, using z as the independent variable. C(z) = mx + k Find a quadratic regression equation for the price-demand data, using e as the independent variable. P-a+ be + cz Round m to 1 decimal place, and round k to the nearest integer. Round a to the nearest integer, round b to 2 decimal places, and round e to 4 decimal places. Profit Model Use the models computed to find a model for the weekly profit, using az as the independent variable. The weekly profit model has roots at z = –52.789, r = 47.555, and z = 202.944, rounded to 3 P(z) -r+uz + sz? + tz decimal places. NOTE: Do not calculate another regression. Use the fact that profit is revenue minus cost. Round r to the nearest integer, round u to1 decimal place, round a to 2 decimal places, and round t The marginal weekly profit model has roots at x = -8.488 and r = to 4 decimal places. 140.295, rounded to 3 decimal places. What weekly production level will maximize profit? Round to 1 decimal place. sleeping bags
Yaster Outhers manutachures and welh estreme-cold sleeping bags The table below shows the price-demand and total cost data where Revenue Model ph the wholesale price in dollan of a sleeping bag for a weekly demand ofsleeping bags Cisthe total cost n dullard of producing sleeping bags Using the regression model computed above, find a model for the weekly revenue, using z as the a sleeping bags independent variable. 1240 13.000 NOTE: Do not calculate another regression Use the price equation to find a model for revenue R(2) -p-a. 20 235 14300 180 155 18.500 R(z)-p-z (a + bz + cz)a ar + ba+e 1220 s0 21.000 Cost Model Find a linear regression model for the weekly cost data, using z as the independent variable. C(z) = mx + k Find a quadratic regression equation for the price-demand data, using e as the independent variable. P-a+ be + cz Round m to 1 decimal place, and round k to the nearest integer. Round a to the nearest integer, round b to 2 decimal places, and round e to 4 decimal places. Profit Model Use the models computed to find a model for the weekly profit, using az as the independent variable. The weekly profit model has roots at z = –52.789, r = 47.555, and z = 202.944, rounded to 3 P(z) -r+uz + sz? + tz decimal places. NOTE: Do not calculate another regression. Use the fact that profit is revenue minus cost. Round r to the nearest integer, round u to1 decimal place, round a to 2 decimal places, and round t The marginal weekly profit model has roots at x = -8.488 and r = to 4 decimal places. 140.295, rounded to 3 decimal places. What weekly production level will maximize profit? Round to 1 decimal place. sleeping bags
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
What weekly production level (number of sleeping bags) will maximize profit?
![**Revenue Model**
To model weekly revenue based on the quantity of sleeping bags produced (denoted as \( x \)), the revenue model \( R(x) \) uses the expression \( R(x) = xp \), where \( p \) is the price.
First, establish a price-demand equation in the form \( p = ax^2 + bx + c \). Then substitute this into the revenue model to find \( R(x) \).
**Cost Model**
Use a linear regression model to represent the weekly cost based on the quantity \( x \), in the form \( C(x) = mx + k \).
- Round \( m \) to one decimal place and \( k \) to the nearest integer.
**Profit Model**
Calculate the weekly profit by subtracting the cost function from the revenue function:
\[ P(x) = R(x) - C(x) \]
- Do not calculate another regression. Use the models found.
- Round to the nearest integer, and use various decimal place rounding as specified.
**Roots of Profit Models**
- **Weekly profit model roots**:
- \( x = -52.789 \)
- \( x = 47.555 \)
- \( x = 202.944 \)
- Rounded to 3 decimal places.
- **Original weekly profit model roots**:
- \( x = 8.488 \)
- \( x = 140.295 \)
- Rounded to 3 decimal places.
**Maximizing Profit**
Determine the weekly production level that will maximize profit. Use the derived models and roots to make this determination.
**Data Table**
The table describes the quantity of sleeping bags produced and associated price and cost values for certain production levels.
**Conclusion**
Apply these models to find the optimal production level of sleeping bags to maximize profit systematically, adhering to rounding rules and using given equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a986e3d-0e42-469e-aac8-a76738ec5c0d%2F297e1102-c066-486e-984e-6b473398ef92%2Fc9zywcf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Revenue Model**
To model weekly revenue based on the quantity of sleeping bags produced (denoted as \( x \)), the revenue model \( R(x) \) uses the expression \( R(x) = xp \), where \( p \) is the price.
First, establish a price-demand equation in the form \( p = ax^2 + bx + c \). Then substitute this into the revenue model to find \( R(x) \).
**Cost Model**
Use a linear regression model to represent the weekly cost based on the quantity \( x \), in the form \( C(x) = mx + k \).
- Round \( m \) to one decimal place and \( k \) to the nearest integer.
**Profit Model**
Calculate the weekly profit by subtracting the cost function from the revenue function:
\[ P(x) = R(x) - C(x) \]
- Do not calculate another regression. Use the models found.
- Round to the nearest integer, and use various decimal place rounding as specified.
**Roots of Profit Models**
- **Weekly profit model roots**:
- \( x = -52.789 \)
- \( x = 47.555 \)
- \( x = 202.944 \)
- Rounded to 3 decimal places.
- **Original weekly profit model roots**:
- \( x = 8.488 \)
- \( x = 140.295 \)
- Rounded to 3 decimal places.
**Maximizing Profit**
Determine the weekly production level that will maximize profit. Use the derived models and roots to make this determination.
**Data Table**
The table describes the quantity of sleeping bags produced and associated price and cost values for certain production levels.
**Conclusion**
Apply these models to find the optimal production level of sleeping bags to maximize profit systematically, adhering to rounding rules and using given equations.
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
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman