Solve The Problem.Find The Break-even Point For The Given Cost And Revenue Equations. Round To The Nearest Whole Unit.$\[ C = 15n + 269,000 \\]$\[ R = 95n \\]Please Select The Best Answer From The Choices Provided:A. 80 B. 3363 C.

Feb 27, 2025 by ADMIN 233 views

**Finding the Break-Even Point: A Step-by-Step Guide**

Introduction

In business, the break-even point (BEP) is a crucial concept that helps entrepreneurs and managers determine the point at which their business becomes profitable. It is the point at which the total revenue equals the total cost, and the business starts to make a profit. In this article, we will explore how to find the break-even point using the given cost and revenue equations.

Understanding the Cost and Revenue Equations

The cost equation is given by:

C = 15n + 269,000

Where C is the total cost and n is the number of units produced.

The revenue equation is given by:

R = 95n

Where R is the total revenue and n is the number of units sold.

Finding the Break-Even Point

To find the break-even point, we need to set the cost equation equal to the revenue equation and solve for n.

C = R

15n + 269,000 = 95n

Subtracting 15n from both sides gives:

269,000 = 80n

Dividing both sides by 80 gives:

n = 3363.75

Since we are asked to round to the nearest whole unit, we round n to 3364.

Conclusion

In conclusion, the break-even point for the given cost and revenue equations is 3364 units. This means that if the business produces and sells 3364 units, the total revenue will equal the total cost, and the business will start to make a profit.

Discussion

The break-even point is an important concept in business because it helps entrepreneurs and managers determine the minimum number of units that need to be sold in order to break even. It is also a useful tool for making decisions about production levels, pricing, and investment.

Real-World Applications

The break-even point has many real-world applications in business. For example, it can be used to:

Determine the minimum number of units that need to be sold in order to break even
Make decisions about production levels and pricing
Evaluate the feasibility of a new product or service
Determine the break-even point for different scenarios, such as changes in production costs or revenue

Example Problems

Here are a few example problems that illustrate how to find the break-even point:

Find the break-even point for the cost equation C = 20n + 100,000 and the revenue equation R = 120n.
Find the break-even point for the cost equation C = 30n + 200,000 and the revenue equation R = 150n.
Find the break-even point for the cost equation C = 40n + 300,000 and the revenue equation R = 180n.

Solutions

For the first example, we set the cost equation equal to the revenue equation and solve for n: 20n + 100,000 = 120n Subtracting 20n from both sides gives: 100,000 = 100n Dividing both sides by 100 gives: n = 1000
For the second example, we set the cost equation equal to the revenue equation and solve for n: 30n + 200,000 = 150n Subtracting 30n from both sides gives: 200,000 = 120n Dividing both sides by 120 gives: n = 1666.67
For the third example, we set the cost equation equal to the revenue equation and solve for n: 40n + 300,000 = 180n Subtracting 40n from both sides gives: 300,000 = 140n Dividing both sides by 140 gives: n = 2142.86

Conclusion

Introduction

In our previous article, we explored how to find the break-even point using the given cost and revenue equations. In this article, we will answer some frequently asked questions about the break-even point.

Q: What is the break-even point?

A: The break-even point is the point at which the total revenue equals the total cost, and the business starts to make a profit.

Q: Why is the break-even point important?

A: The break-even point is important because it helps entrepreneurs and managers determine the minimum number of units that need to be sold in order to break even. It is also a useful tool for making decisions about production levels, pricing, and investment.

Q: How do I find the break-even point?

A: To find the break-even point, you need to set the cost equation equal to the revenue equation and solve for n. The cost equation is given by C = 15n + 269,000 and the revenue equation is given by R = 95n.

Q: What if I have a variable cost and a fixed cost?

A: If you have a variable cost and a fixed cost, you need to add the fixed cost to the cost equation and subtract it from the revenue equation. For example, if the variable cost is 15n and the fixed cost is 269,000, the cost equation would be C = 15n + 269,000.

Q: What if I have a different revenue equation?

A: If you have a different revenue equation, you need to substitute it into the break-even point formula and solve for n. For example, if the revenue equation is R = 120n, you would substitute it into the break-even point formula and solve for n.

Q: Can I use the break-even point formula for different scenarios?

A: Yes, you can use the break-even point formula for different scenarios. For example, you can use it to determine the break-even point for different production levels, pricing, and investment scenarios.

Q: How do I calculate the break-even point for a product with a high fixed cost?

A: To calculate the break-even point for a product with a high fixed cost, you need to add the fixed cost to the cost equation and subtract it from the revenue equation. For example, if the fixed cost is 500,000, you would add it to the cost equation and subtract it from the revenue equation.

Q: Can I use the break-even point formula for a service-based business?

A: Yes, you can use the break-even point formula for a service-based business. However, you need to consider the variable and fixed costs associated with providing the service.

Q: How do I calculate the break-even point for a business with multiple products?

A: To calculate the break-even point for a business with multiple products, you need to calculate the break-even point for each product separately and then combine them.

Conclusion

In conclusion, the break-even point is an important concept in business that helps entrepreneurs and managers determine the minimum number of units that need to be sold in order to break even. By understanding how to find the break-even point, businesses can make informed decisions and achieve their goals.

Additional Resources

Break-Even Point Formula: C = R
Cost Equation: C = 15n + 269,000
Revenue Equation: R = 95n
Break-Even Point Calculator: [insert link]
Break-Even Point Examples: [insert link]

Frequently Asked Questions

Q: What is the break-even point? A: The break-even point is the point at which the total revenue equals the total cost, and the business starts to make a profit.
Q: Why is the break-even point important? A: The break-even point is important because it helps entrepreneurs and managers determine the minimum number of units that need to be sold in order to break even.
Q: How do I find the break-even point? A: To find the break-even point, you need to set the cost equation equal to the revenue equation and solve for n.