A manufacturer of DVD players has weekly fixed costs of $1,520 and variable costs of $12.50 per units for one particular model. The company sells this model to dealers for $19.50 each.
Match the statement with the correct answer.

Write the function for the weekly total costs, C(x).
---Select---
Write the function for the total revenue function, R(x).
---Select---
Write the function for the profit function, P(x).
---Select---
This is the cost (in dollars) of producing 150 DVD players.
---Select---
This is the profit (in dollars) when 150 DVD players are sold but since it is negative it means that the company loses money when 150 DVD players are sold.
---Select---
Each additional DVD player sold increases the profit by this many dollars.
---Select---
This is the revenue (in dollars) generated from the sale of 150 DVD players.
---Select---

Let's break down the components to match each part of the problem with the correct answer. We'll define the functions and evaluate them based on the given information.

### Given:
- **Fixed costs (weekly):** $1,520
- **Variable costs per unit:** $12.50
- **Selling price per unit:** $19.50

### 1. Write the function for the weekly total costs, $ C(x) $:
The total cost function includes both fixed costs and variable costs. The formula is:
\[
C(x) = \text{Fixed costs} + (\text{Variable cost per unit} \times \text{Number of units})
\]
\[
C(x) = 1,520 + 12.50x
\]
So, the total cost function is:
\[
C(x) = 1,520 + 12.50x
\]

### 2. Write the function for the total revenue function, $ R(x) $:
Revenue is calculated by multiplying the number of units sold by the selling price per unit. The formula is:
\[
R(x) = \text{Selling price per unit} \times \text{Number of units}
\]
\[
R(x) = 19.50x
\]
So, the total revenue function is:
\[
R(x) = 19.50x
\]

### 3. Write the function for the profit function, $ P(x) $:
Profit is calculated as total revenue minus total costs. The formula is:
\[
P(x) = R(x) - C(x)
\]
\[
P(x) = 19.50x - (1,520 + 12.50x)
\]
Simplifying:
\[
P(x) = 19.50x - 1,520 - 12.50x
\]
\[
P(x) = 7x - 1,520
\]
So, the profit function is:
\[
P(x) = 7x - 1,520
\]

### 4. The cost (in dollars) of producing 150 DVD players:
To find the cost for producing 150 DVD players, substitute $ x = 150 $ into the cost function $ C(x) $:
\[
C(150) = 1,520 + 12.50(150)
\]
\[
C(150) = 1,520 + 1,875 = 3,395
\]
So, the cost of producing 150 DVD players is **$3,395**.

### 5. The profit (in dollars) when 150 DVD players are sold:
To find the profit when 150 DVD players are sold, substitute $ x = 150 $ into the profit function $ P(x) $:
\[
P(150) = 7(150) - 1,520
\]
\[
P(150) = 1,050 - 1,520 = -470
\]
So, the company loses **$470** when selling 150 DVD players.

### 6. Each additional DVD player sold increases the profit by this many dollars:
The profit per additional DVD player is the coefficient of $ x $ in the profit function $ P(x) = 7x - 1,520 $, which is **$7**.

### 7. The revenue (in dollars) generated from the sale of 150 DVD players:
To find the revenue when 150 DVD players are sold, substitute $ x = 150 $ into the revenue function $ R(x) $:
\[
R(150) = 19.50(150)
\]
\[
R(150) = 2,925
\]
So, the revenue generated from selling 150 DVD players is **$2,925**.

---

### Summary:
1. The total cost function: $ C(x) = 1,520 + 12.50x $
2. The total revenue function: $ R(x) = 19.50x $
3. The profit function: $ P(x) = 7x - 1,520 $
4. The cost of producing 150 DVD players: **$3,395**
5. The profit (or loss) when 150 DVD players are sold: **-$470** (loss)
6. Each additional DVD player sold increases the profit by: **$7**
7. The revenue generated from selling 150 DVD players: **$2,925**

---

Do you need further details or have any questions?  
Here are 5 related questions to expand this concept:
1. How many DVD players must the company sell to break even?
2. What is the company's profit if they sell 500 DVD players in a week?
3. How would a change in the fixed costs affect the break-even point?
4. What is the marginal cost of producing each additional DVD player?
5. If the selling price is increased to $22.50, what happens to the profit function?

**Tip:** In cost-profit analysis, understanding the break-even point helps determine when revenue covers all costs, resulting in zero profit or loss.

A manufacturer of DVD players has weekly fixed costs of $1,520 and variable costs of $12.50 per units for one particular model. The company sells this model to dealers for $19.50 each.
Match the statement with the correct answer.
Write the function for the weekly total costs, C(x).
Write the function for the total revenue function, R(x).
Write the function for the profit function, P(x).
This is the cost (in dollars) of producing 150 DVD players.
This is the profit (in dollars) when 150 DVD players are sold but since it is negative it means that the company loses money when 150 DVD players are sold.
Each additional DVD player sold increases the profit by this many dollars.
This is the revenue (in dollars) generated from the sale of 150 DVD players.

Learn how to calculate the cost, revenue, and profit functions for a DVD player manufacturing company with fixed and variable costs. This problem includes linear functions for total cost, revenue, and profit, and analyzes a scenario of producing and selling 150 DVD players. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation