Find the break-even point for the firm whose cost function C and revenue function R are given.
C(x) = 210x + 20,000; R(x) = 360x

To find the break-even point, we need to determine when the firm's cost function \( C(x) \) equals its revenue function \( R(x) \). This happens when:

\[
C(x) = R(x)
\]

Given:
- Cost function: \( C(x) = 210x + 20,000 \)
- Revenue function: \( R(x) = 360x \)

Set the two functions equal to each other:

\[
210x + 20,000 = 360x
\]

Now, solve for \( x \):

1. Subtract \( 210x \) from both sides:

\[
20,000 = 150x
\]

2. Divide both sides by 150:

\[
x = \frac{20,000}{150} = 133.33
\]

So, the break-even point occurs when \( x = 133.33 \). This means the firm needs to sell approximately 134 units to break even.

### Do you want more details or have any questions?

Here are 5 related questions you might want to explore:
1. What is the profit function for the firm?
2. How much revenue does the firm earn at the break-even point?
3. What is the total cost at the break-even point?
4. How would the break-even point change if the fixed cost increased?
5. What happens if the price per unit decreases?

**Tip:** The break-even point is critical for understanding when a business covers its costs and starts making a profit.

Find the break-even point for the firm whose cost function C and revenue function R are given. C(x) = 210x + 20,000; R(x) = 360x

Learn how to find the break-even point for a firm using cost and revenue functions. This problem involves key algebraic concepts, such as solving linear equations and understanding break-even analysis. 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