A corporation sells bicylce pump. Each pump sells for $9 and the variable cost of producing each unit is 40% of the selling price. The montly fixed costs incurred by the division are $50,000. What is the break even point for the division?

To determine the **break-even point**, we need to calculate the number of bicycle pumps the corporation must sell to cover all costs (fixed and variable) without making a profit or a loss.

The **formula for the break-even point** in units is:

\[
\text{Break-even point (units)} = \frac{\text{Fixed Costs}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}}
\]

### Given dataTo determine the **break-even point**, we need to calculate the number of bicycle pumps the corporation must sell to cover all costs (fixed and variable) without making a profit or a loss.

The **formula for the break-even point** in units is:

\[
\text{Break-even point (units)} = \frac{\text{Fixed Costs}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}}
\]

### Given 
- **Selling price per unit** = $9
- **Variable cost per unit** = 40% of the selling price = $0.4 \times 9 = 3.60$
- **Fixed costs** = $50,000

### Step-by-step solution:
1. **Contribution margin per unit**:
\[
\text{Contribution margin} = \text{Selling price per unit} - \text{Variable cost per unit}
\]
\[
\text{Contribution margin} = 9 - 3.60 = 5.40
\]

2. **Break-even point in units**:
\[
\text{Break-even point (units)} = \frac{50,000}{5.40} \approx 9259.26
\]

Since the number of units cannot be fractional, we round up:
\[
\text{Break-even point} = 9260 \text{ units}
\]

### Conclusion:
The corporation needs to sell **9260 bicycle pumps** to break even.

Would you like further details or have any questions?

### Relative questions:
1. What happens if the selling price of each pump increases?
2. How does a change in fixed costs affect the break-even point?
3. What is the impact of reducing the variable cost per unit on profitability?
4. Can the break-even point be reduced by increasing sales volume?
5. How do you calculate the break-even point in dollars rather than units?

**Tip:** Break-even analysis is a useful tool for understanding how sales, costs, and pricing interact to affect profitability.

A corporation sells bicycle pumps. Each pump sells for $9 and the variable cost of producing each unit is 40% of the selling price. The monthly fixed costs incurred by the division are $50,000. What is the break-even point for the division?

Learn how to calculate the break-even point for a corporation selling bicycle pumps. With a selling price of $9 per unit, a variable cost of 40% of the selling price, and monthly fixed costs of $50,000, we explore how many units must be sold to break even. This detailed step-by-step guide covers break-even analysis and cost analysis concepts, suitable for students in Grades 9-12.

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