The manager of a fumiture factory finds that it costs $2200 to produce 100 chairs in one day and $5400 to produce 300 chairs in one day. (a) Assuming that the relationship between cost and the number of chairs produced is linear, find a linear function C that models the cost of producing x cha C(x) = (b) Draw a graph of c. 10000- 10000 9000 s000 9000 so0 7000 7000 6000 6000 5000 5000 4000 4000 3000 3000 2000 2000 1000 1000
The manager of a fumiture factory finds that it costs $2200 to produce 100 chairs in one day and $5400 to produce 300 chairs in one day. (a) Assuming that the relationship between cost and the number of chairs produced is linear, find a linear function C that models the cost of producing x cha C(x) = (b) Draw a graph of c. 10000- 10000 9000 s000 9000 so0 7000 7000 6000 6000 5000 5000 4000 4000 3000 3000 2000 2000 1000 1000
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.5: Linear Functions And Models
Problem 50E: Manufacturing Cost The manager of a furniture factory finds that it costs 2200 to produce 100 chairs...
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![### Linear Cost Analysis of Chair Production in a Furniture Factory
The manager of a furniture factory observes the following costs associated with chair production:
- It costs $2200 to produce 100 chairs in one day.
- It costs $5400 to produce 300 chairs in one day.
**(a) Assuming a linear relationship between cost and the number of chairs produced, derive a linear function \( C(x) \) that represents the cost (\( C \)) of producing \( x \) chairs in one day.**
\[ C(x) = \]
**(b) Draw the graph of \( C(x) \).**
Below are four different graphs depicting potential linear relationships. Analyze the correct one based on the given data:
1. 
- A linear increasing graph starting from the origin and extending to the coordinate (600, 10000).
2. 
- A decreasing linear line beginning at (100, 5400) and intersecting the x-axis.
3. 
- An increasing linear graph starting from (100, 2200) and extending upwards through (400, 7000).
4. 
- A linear increasing graph beginning slightly above zero and continuing upwards.
**Identify the correct graph based on the starting and data points provided.**
**(c) Determine the slope of the linear function.**
---
### Problem Breakdown
- **Interpretation:**
- The relationship between cost and number of chairs is linear.
- The cost function \( C(x) \) where \( x \) is the number of chairs produced.
- **Calculation of Slope:**
- Use the points (100, 2200) and (300, 5400).
\[ \text{Slope (m)} = \frac{\Delta \text{Cost}}{\Delta \text{Chairs}} = \frac{5400 - 2200}{300 - 100} \]
\[ m = \frac{3200}{200} = 16 \]
The slope of the line, \( m \), indicates that the cost increases by $16 for each additional chair produced.
**(c) Calculate the cost increase rate:**
\[ \text{Rate of Cost Increase} = \$ \text{ per chair} \] [Fill in the calculated slope above]
---
Use these](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c273fa9-f695-4738-9feb-47913b6fbc7e%2Fc2c75a69-2411-4981-aa29-56ae2e187b76%2Fb6ux6th_processed.png&w=3840&q=75)
Transcribed Image Text:### Linear Cost Analysis of Chair Production in a Furniture Factory
The manager of a furniture factory observes the following costs associated with chair production:
- It costs $2200 to produce 100 chairs in one day.
- It costs $5400 to produce 300 chairs in one day.
**(a) Assuming a linear relationship between cost and the number of chairs produced, derive a linear function \( C(x) \) that represents the cost (\( C \)) of producing \( x \) chairs in one day.**
\[ C(x) = \]
**(b) Draw the graph of \( C(x) \).**
Below are four different graphs depicting potential linear relationships. Analyze the correct one based on the given data:
1. 
- A linear increasing graph starting from the origin and extending to the coordinate (600, 10000).
2. 
- A decreasing linear line beginning at (100, 5400) and intersecting the x-axis.
3. 
- An increasing linear graph starting from (100, 2200) and extending upwards through (400, 7000).
4. 
- A linear increasing graph beginning slightly above zero and continuing upwards.
**Identify the correct graph based on the starting and data points provided.**
**(c) Determine the slope of the linear function.**
---
### Problem Breakdown
- **Interpretation:**
- The relationship between cost and number of chairs is linear.
- The cost function \( C(x) \) where \( x \) is the number of chairs produced.
- **Calculation of Slope:**
- Use the points (100, 2200) and (300, 5400).
\[ \text{Slope (m)} = \frac{\Delta \text{Cost}}{\Delta \text{Chairs}} = \frac{5400 - 2200}{300 - 100} \]
\[ m = \frac{3200}{200} = 16 \]
The slope of the line, \( m \), indicates that the cost increases by $16 for each additional chair produced.
**(c) Calculate the cost increase rate:**
\[ \text{Rate of Cost Increase} = \$ \text{ per chair} \] [Fill in the calculated slope above]
---
Use these
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