A newly opened bed-and-breakfast projects the following: Monthly fixed costs Variable cost per occupied room per night $60 Revenue per occupied room per night $10000 $165 How many rooms would have to be occupied per month in order to break even?

MATLAB: An Introduction with Applications
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**Problem Scenario: Bed-and-Breakfast Break-Even Analysis**

A newly opened bed-and-breakfast projects the following:

- **Monthly fixed costs:** $10,000
- **Variable cost per occupied room per night:** $60
- **Revenue per occupied room per night:** $165

**Question:**  
How many rooms would have to be occupied per month in order to break even?

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**Solution Explanation:**

To find the break-even point, use the break-even formula:

\[ \text{Break-even point (in rooms)} = \frac{\text{Fixed Costs}}{\text{Revenue per Room} - \text{Variable Cost per Room}} \]

\[ \text{Break-even point (in rooms)} = \frac{10,000}{165 - 60} \]

\[ \text{Break-even point (in rooms)} = \frac{10,000}{105} \]

\[ \text{Break-even point (in rooms)} \approx 95.24 \]

Thus, approximately **96 rooms** need to be occupied per month to break even, as you must round up to the nearest whole number since you can't occupy a fraction of a room.
Transcribed Image Text:**Problem Scenario: Bed-and-Breakfast Break-Even Analysis** A newly opened bed-and-breakfast projects the following: - **Monthly fixed costs:** $10,000 - **Variable cost per occupied room per night:** $60 - **Revenue per occupied room per night:** $165 **Question:** How many rooms would have to be occupied per month in order to break even? --- **Solution Explanation:** To find the break-even point, use the break-even formula: \[ \text{Break-even point (in rooms)} = \frac{\text{Fixed Costs}}{\text{Revenue per Room} - \text{Variable Cost per Room}} \] \[ \text{Break-even point (in rooms)} = \frac{10,000}{165 - 60} \] \[ \text{Break-even point (in rooms)} = \frac{10,000}{105} \] \[ \text{Break-even point (in rooms)} \approx 95.24 \] Thus, approximately **96 rooms** need to be occupied per month to break even, as you must round up to the nearest whole number since you can't occupy a fraction of a room.
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