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.