Yaster Outfitters manufactures and sells extreme-cold sleeping bags. The table below shows the price-demand and total cost data, where: Revenue Model • pis the wholesale price (in dollars) of a sleeping bag for a weekly demand of a sleeping bags: . Cis the total cost (in dollars) of producing z sleeping bags. Using the regression model independent variable. z (sleeping bags) P (S) C (S) 95 240 13.000 NOTE: Do not calculate ano 120 235 14,300 R(x) =p- r. 180 155 18.500 220 50 21.000 R(x)
Yaster Outfitters manufactures and sells extreme-cold sleeping bags. The table below shows the price-demand and total cost data, where: Revenue Model • pis the wholesale price (in dollars) of a sleeping bag for a weekly demand of a sleeping bags: . Cis the total cost (in dollars) of producing z sleeping bags. Using the regression model independent variable. z (sleeping bags) P (S) C (S) 95 240 13.000 NOTE: Do not calculate ano 120 235 14,300 R(x) =p- r. 180 155 18.500 220 50 21.000 R(x)
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
What is maximum weekly profit?
![### Profit Model
Use the models computed to find a model of the weekly profit using \( x \) as the independent variable.
\[ P(x) = x^3 + x^2 - 42x + 96 \]
**Note:** No calculator regression. Use the fact that profit revenue minus cost.
The original form of the weekly profit model has roots at \( x = -5.26709, x = -1.74555, \) and \( x = 202.944 \), rounded to 3 decimal places.
The adjusted form of the weekly profit model has roots at \( x = -8.9488 \) and \( x = 140.295 \), rounded to 3 decimal places.
### What is the maximum weekly profit? Round to the nearest dollar.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a986e3d-0e42-469e-aac8-a76738ec5c0d%2Fc999c2a6-1eb9-41df-8b80-5a1be8b1521f%2Fnap1uza.jpeg&w=3840&q=75)
Transcribed Image Text:### Profit Model
Use the models computed to find a model of the weekly profit using \( x \) as the independent variable.
\[ P(x) = x^3 + x^2 - 42x + 96 \]
**Note:** No calculator regression. Use the fact that profit revenue minus cost.
The original form of the weekly profit model has roots at \( x = -5.26709, x = -1.74555, \) and \( x = 202.944 \), rounded to 3 decimal places.
The adjusted form of the weekly profit model has roots at \( x = -8.9488 \) and \( x = 140.295 \), rounded to 3 decimal places.
### What is the maximum weekly profit? Round to the nearest dollar.
![**Vaster Outfitters manufactures and sells extreme-cold sleeping bags.**
The table below shows the price-demand and total cost data, where:
- \( p \) is the wholesale price (in dollars) of a sleeping bag for a weekly demand of \( x \) sleeping bags.
- \( C \) is the total cost (in dollars) of producing \( x \) sleeping bags.
| \( x \) (sleeping bags) | \( p \) | \( C \) |
|------------------|-------|------|
| 120 | 245 | 13,000 |
| 150 | 220 | 15,000 |
| 180 | 195 | 17,100 |
| 200 | 155 | 18,500 |
| 220 | 105 | 21,000 |
---
### Revenue Model
Using the regression model computed above, find a model for the weekly revenue, using \( x \) as the independent variable.
**NOTE:** Do not calculate another regression. Use the price equation to find a model for revenue.
\[ R(x) = p \cdot x = (a + bx + cx^2)x = ax + bx^2 + cx^3 \]
### Cost Model
Find a quadratic regression equation for the price-demand data, using \( x \) as the independent variable:
\[ p = a + bx + cx^2 \]
Round \( a \) to the nearest integer, round \( b \) to 2 decimal places, and round \( c \) to 4 decimal places.
Find a linear regression model for the weekly cost data, using \( x \) as the independent variable.
\[ C(x) = mx + k \]
Round \( m \) to 1 decimal place, and round \( k \) to the nearest integer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a986e3d-0e42-469e-aac8-a76738ec5c0d%2Fc999c2a6-1eb9-41df-8b80-5a1be8b1521f%2Fxlj05l1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Vaster Outfitters manufactures and sells extreme-cold sleeping bags.**
The table below shows the price-demand and total cost data, where:
- \( p \) is the wholesale price (in dollars) of a sleeping bag for a weekly demand of \( x \) sleeping bags.
- \( C \) is the total cost (in dollars) of producing \( x \) sleeping bags.
| \( x \) (sleeping bags) | \( p \) | \( C \) |
|------------------|-------|------|
| 120 | 245 | 13,000 |
| 150 | 220 | 15,000 |
| 180 | 195 | 17,100 |
| 200 | 155 | 18,500 |
| 220 | 105 | 21,000 |
---
### Revenue Model
Using the regression model computed above, find a model for the weekly revenue, using \( x \) as the independent variable.
**NOTE:** Do not calculate another regression. Use the price equation to find a model for revenue.
\[ R(x) = p \cdot x = (a + bx + cx^2)x = ax + bx^2 + cx^3 \]
### Cost Model
Find a quadratic regression equation for the price-demand data, using \( x \) as the independent variable:
\[ p = a + bx + cx^2 \]
Round \( a \) to the nearest integer, round \( b \) to 2 decimal places, and round \( c \) to 4 decimal places.
Find a linear regression model for the weekly cost data, using \( x \) as the independent variable.
\[ C(x) = mx + k \]
Round \( m \) to 1 decimal place, and round \( k \) to the nearest integer.
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