Gareth Has Just Remodeled His Kitchen And Wants To Buy One Of Two Stand-alone Freezers. Consider The Following Table, Which Displays The Prices, Electricity Costs, And Lifespans Of The Two Freezers He Is
Introduction
Gareth has just remodeled his kitchen and is in the market for a new stand-alone freezer. After researching two popular models, he is torn between which one to purchase. To make an informed decision, Gareth needs to consider various factors such as price, electricity costs, and lifespan. In this article, we will analyze the data provided in the table below and use mathematical concepts to help Gareth make a decision.
Table: Stand-Alone Freezer Comparison
| Model | Price (USD) | Electricity Cost (USD/year) | Lifespan (years) |
|---|---|---|---|
| A | 800 | 150 | 10 |
| B | 1000 | 120 | 12 |
Total Cost of Ownership
To determine the total cost of ownership for each freezer, we need to consider the initial purchase price, electricity costs, and lifespan. The total cost of ownership can be calculated using the following formula:
Total Cost of Ownership = (Price + (Electricity Cost * Lifespan)) / Lifespan
Let's calculate the total cost of ownership for each freezer:
Model A
Total Cost of Ownership = (800 + (150 * 10)) / 10 = (800 + 1500) / 10 = 2300 / 10 = 230
Model B
Total Cost of Ownership = (1000 + (120 * 12)) / 12 = (1000 + 1440) / 12 = 2440 / 12 = 203.33
Comparison of Total Cost of Ownership
Based on the calculations above, we can see that Model B has a lower total cost of ownership compared to Model A. This is because Model B has a longer lifespan and lower electricity costs.
Break-Even Analysis
To determine when the cost of Model B will be equal to the cost of Model A, we can use the break-even analysis formula:
Break-Even Point = (Price of Model A - Price of Model B) / (Electricity Cost of Model B - Electricity Cost of Model A)
Let's calculate the break-even point:
Break-Even Point = (800 - 1000) / (120 - 150) = -200 / -30 = 6.67 years
This means that if Gareth plans to use the freezer for more than 6.67 years, Model B will be the more cost-effective option.
Conclusion
In conclusion, our mathematical analysis has shown that Model B is the more cost-effective option for Gareth. With a lower total cost of ownership and a longer lifespan, Model B is the better choice for those who plan to use the freezer for an extended period. However, if Gareth only plans to use the freezer for a short period, Model A may be a more suitable option.
Recommendation
Based on our analysis, we recommend that Gareth purchase Model B. With its lower total cost of ownership and longer lifespan, Model B is the more cost-effective option for those who plan to use the freezer for an extended period.
Future Research Directions
In future research, we can explore other factors that may affect the total cost of ownership, such as maintenance costs, repair costs, and environmental impact. Additionally, we can use more advanced mathematical models, such as decision trees and sensitivity analysis, to further analyze the data and provide more accurate recommendations.
Limitations
One limitation of our analysis is that we have assumed that the electricity costs and lifespan of the freezers remain constant over time. In reality, these costs may vary depending on various factors, such as changes in electricity prices and usage patterns. Therefore, our analysis should be taken as a rough estimate rather than a precise calculation.
Conclusion
Q: What is the total cost of ownership for each freezer?
A: The total cost of ownership for Model A is $230, while the total cost of ownership for Model B is $203.33.
Q: Which freezer has a longer lifespan?
A: Model B has a longer lifespan of 12 years, while Model A has a lifespan of 10 years.
Q: How long will it take for the cost of Model B to be equal to the cost of Model A?
A: Based on our break-even analysis, it will take approximately 6.67 years for the cost of Model B to be equal to the cost of Model A.
Q: What are the electricity costs for each freezer?
A: The electricity cost for Model A is $150 per year, while the electricity cost for Model B is $120 per year.
Q: What is the initial purchase price of each freezer?
A: The initial purchase price of Model A is $800, while the initial purchase price of Model B is $1000.
Q: How can I calculate the total cost of ownership for each freezer?
A: To calculate the total cost of ownership for each freezer, you can use the following formula:
Total Cost of Ownership = (Price + (Electricity Cost * Lifespan)) / Lifespan
Q: What are the limitations of this analysis?
A: One limitation of this analysis is that we have assumed that the electricity costs and lifespan of the freezers remain constant over time. In reality, these costs may vary depending on various factors, such as changes in electricity prices and usage patterns.
Q: Can I use this analysis to compare other freezers?
A: Yes, you can use this analysis to compare other freezers by plugging in the relevant data for each freezer. However, keep in mind that the results may vary depending on the specific characteristics of each freezer.
Q: What are some other factors that I should consider when choosing a freezer?
A: Some other factors that you should consider when choosing a freezer include:
- Maintenance costs: Consider the cost of replacing parts and performing maintenance on the freezer.
- Repair costs: Consider the cost of repairing the freezer if it breaks down.
- Environmental impact: Consider the environmental impact of the freezer, including its energy efficiency and any potential environmental hazards.
- Features: Consider the features of the freezer, including its capacity, temperature control, and any additional features such as ice makers or water dispensers.
Q: How can I use this analysis to make a decision?
A: To use this analysis to make a decision, consider the following steps:
- Determine your budget: Decide how much you are willing to spend on a freezer.
- Consider your needs: Think about your needs and how they will impact your decision.
- Compare the freezers: Use the analysis to compare the freezers and determine which one is the best fit for your needs and budget.
- Make a decision: Based on your analysis, make a decision about which freezer to purchase.
Conclusion
In conclusion, this FAQ article has provided answers to some of the most frequently asked questions about the analysis. We hope that this information has been helpful in making a decision about which freezer to purchase.