A sales person makes a base salary of $400 per week plus 12% commission on sales. (a) Write a linear function to model the sales person's weekly salary S (x) for x dollars in sales. (b) Evaluate S (6000) and interpret the meaning in the context of this problem. Part: 0/2 Part 1 of 2 (a) The linear function is S (x) = for x 0.
A sales person makes a base salary of $400 per week plus 12% commission on sales. (a) Write a linear function to model the sales person's weekly salary S (x) for x dollars in sales. (b) Evaluate S (6000) and interpret the meaning in the context of this problem. Part: 0/2 Part 1 of 2 (a) The linear function is S (x) = for x 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Salesperson Salary Problem
A salesperson makes a base salary of $400 per week plus a 12% commission on sales.
#### Questions:
**(a)** Write a linear function to model the salesperson's weekly salary \( S(x) \) for \( x \) dollars in sales.
**(b)** Evaluate \( S(6000) \) and interpret the meaning in the context of this problem.
#### Solutions:
**Part 1:**
(a) The linear function \( S(x) \) is:
\[ S(x) = 400 + 0.12x \quad \text{for} \quad x \geq 0. \]
**Part 2:**
(b) To evaluate \( S(6000) \), substitute \( x = 6000 \) into the function \( S(x) \):
\[ S(6000) = 400 + 0.12 \times 6000 = 400 + 720 = 1120. \]
**Interpretation:**
When the salesperson makes $6000 in sales, their weekly salary will be $1120.
#### Graphs and Diagrams
- There are no graphs or diagrams provided in this example.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98398fcd-aa3b-4aac-8dda-e0ea37100738%2F63027379-3783-43f9-86e7-52764209b9fb%2Fpck3t4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Salesperson Salary Problem
A salesperson makes a base salary of $400 per week plus a 12% commission on sales.
#### Questions:
**(a)** Write a linear function to model the salesperson's weekly salary \( S(x) \) for \( x \) dollars in sales.
**(b)** Evaluate \( S(6000) \) and interpret the meaning in the context of this problem.
#### Solutions:
**Part 1:**
(a) The linear function \( S(x) \) is:
\[ S(x) = 400 + 0.12x \quad \text{for} \quad x \geq 0. \]
**Part 2:**
(b) To evaluate \( S(6000) \), substitute \( x = 6000 \) into the function \( S(x) \):
\[ S(6000) = 400 + 0.12 \times 6000 = 400 + 720 = 1120. \]
**Interpretation:**
When the salesperson makes $6000 in sales, their weekly salary will be $1120.
#### Graphs and Diagrams
- There are no graphs or diagrams provided in this example.
![### Costs and Pricing in Production
In this module, we will explore the fixed and variable costs required to produce an item, alongside the price at which the item is sold. We begin by defining key terms and applying them to a practical example.
#### Definitions:
1. **Fixed Cost:** This is a cost that does not change with the number of items produced. It remains constant irrespective of the production volume.
2. **Variable Cost per Item:** This cost varies directly with the number of items produced. It increases linearly as more items are produced.
3. **Price at which the Item is Sold:** This is the selling price for each item produced.
#### Example:
- **Fixed Cost:** $4180
- **Variable Cost per Item:** $33.30
- **Price at which the Item is Sold:** $35.30
### Objective:
(a) **Formulate a Linear Cost Function:**
A linear cost function \( C(x) \) represents the total cost to produce \( x \) items. The general form of a linear cost function is given by:
\[ C(x) = Fixed\ Cost + (Variable\ Cost\ per\ Item \times Number\ of\ Items) \]
Using the given values:
1. **Fixed Cost (FC):** $4180
2. **Variable Cost per Item (VC):** $33.30
The linear cost function \( C(x) \) can be written as:
\[ C(x) = 4180 + 33.30x \]
#### Interactive Question:
**Part 1 of 4**
(a) Write a linear cost function that represents the cost \( C(x) \) to produce \( x \) items.
**Solution:**
The linear cost function is \[ C(x) = \] \( \_\_\_\_\_\_\_\_ \) [Input box for 4180 + 33.30x]
### Explanation of Interface:
The interface includes a progress bar indicating your completion of the parts, with the current part being highlighted. In this part, you are required to formulate the linear cost function using the given fixed and variable costs. Enter your answer in the provided input box.
Understanding and constructing cost functions is crucial for effective budgeting and forecasting in production economics. By mastering this concept, you can better predict total costs and inform pricing strategies to ensure profitability.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98398fcd-aa3b-4aac-8dda-e0ea37100738%2F63027379-3783-43f9-86e7-52764209b9fb%2F5rp4x664_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Costs and Pricing in Production
In this module, we will explore the fixed and variable costs required to produce an item, alongside the price at which the item is sold. We begin by defining key terms and applying them to a practical example.
#### Definitions:
1. **Fixed Cost:** This is a cost that does not change with the number of items produced. It remains constant irrespective of the production volume.
2. **Variable Cost per Item:** This cost varies directly with the number of items produced. It increases linearly as more items are produced.
3. **Price at which the Item is Sold:** This is the selling price for each item produced.
#### Example:
- **Fixed Cost:** $4180
- **Variable Cost per Item:** $33.30
- **Price at which the Item is Sold:** $35.30
### Objective:
(a) **Formulate a Linear Cost Function:**
A linear cost function \( C(x) \) represents the total cost to produce \( x \) items. The general form of a linear cost function is given by:
\[ C(x) = Fixed\ Cost + (Variable\ Cost\ per\ Item \times Number\ of\ Items) \]
Using the given values:
1. **Fixed Cost (FC):** $4180
2. **Variable Cost per Item (VC):** $33.30
The linear cost function \( C(x) \) can be written as:
\[ C(x) = 4180 + 33.30x \]
#### Interactive Question:
**Part 1 of 4**
(a) Write a linear cost function that represents the cost \( C(x) \) to produce \( x \) items.
**Solution:**
The linear cost function is \[ C(x) = \] \( \_\_\_\_\_\_\_\_ \) [Input box for 4180 + 33.30x]
### Explanation of Interface:
The interface includes a progress bar indicating your completion of the parts, with the current part being highlighted. In this part, you are required to formulate the linear cost function using the given fixed and variable costs. Enter your answer in the provided input box.
Understanding and constructing cost functions is crucial for effective budgeting and forecasting in production economics. By mastering this concept, you can better predict total costs and inform pricing strategies to ensure profitability.
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