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?
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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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?
---
**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F020bb284-1991-412e-9b5e-60f030c8d0e6%2F95845978-ed2c-45a1-aac0-6ea06f412be4%2Fadtj0m8_processed.png&w=3840&q=75)
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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