Suppose that a firm manufactures espresso machines. The firm's fixed cost is $1,450,220, and the variable cost is $86 per machine. If each machine sells for $332, how many espresso machines need to be sold to break even? 

To determine the break-even point, we need to calculate how many espresso machines need to be sold for the firm to cover both its fixed and variable costs.

### Formula for break-even point:

\[
\text{Break-even point (units)} = \frac{\text{Fixed cost}}{\text{Selling price per unit} - \text{Variable cost per unit}}
\]

### Given dataTo determine the break-even point, we need to calculate how many espresso machines need to be sold for the firm to cover both its fixed and variable costs.

### Formula for break-even point:

\[
\text{Break-even point (units)} = \frac{\text{Fixed cost}}{\text{Selling price per unit} - \text{Variable cost per unit}}
\]

### Given 
- Fixed cost (FC) = $1,450,220
- Variable cost per machine (VC) = $86
- Selling price per machine (SP) = $332

### Substituting values into the formula:

\[
\text{Break-even point (units)} = \frac{1,450,220}{332 - 86}
\]

First, calculate the difference between the selling price and the variable cost:

\[
332 - 86 = 246
\]

Now, compute the break-even point:

\[
\text{Break-even point (units)} = \frac{1,450,220}{246} \approx 5,895
\]

### Conclusion:
The firm needs to sell approximately **5,895 espresso machines** to break even.

Do you want more details or have any questions?

Here are some related questions for deeper understanding:
1. What is the total cost of producing 5,895 espresso machines?
2. How much profit will the firm make if they sell 6,500 machines?
3. What happens to the break-even point if the variable cost increases?
4. How would a change in the selling price impact the break-even point?
5. What are the benefits of reducing fixed costs in this scenario?

**Tip:** Understanding break-even analysis helps businesses decide pricing strategies and cost management approaches.

Suppose that a firm manufactures espresso machines. The firm's fixed cost is $1,450,220, and the variable cost is $86 per machine. If each machine sells for $332, how many espresso machines need to be sold to break even?

Learn how to calculate the break-even point for a firm manufacturing espresso machines. Given a fixed cost of $1,450,220 and a variable cost of $86 per machine, this problem explores how many machines need to be sold at $332 each to break even. Suitable for Grades 10-12, this step-by-step solution covers key concepts in algebra and cost management.

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