Pam Has Just Moved Into A New Home And Wants To Purchase An Oven. She Expects To Live In This House For The Foreseeable Future. She Has Narrowed Her Choices Down To Two Options. Consider The Following Table, Which Describes The Prices, Daily

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Pam's Oven Purchase Decision: A Mathematical Analysis

Pam has just moved into a new home and is in the process of purchasing an oven. She has narrowed her choices down to two options and is trying to make a decision based on their prices and expected lifetimes. In this article, we will analyze the situation mathematically and provide Pam with a framework to make an informed decision.

Pam has two oven options to choose from: Oven A and Oven B. The prices and expected lifetimes of the ovens are as follows:

Oven Price Expected Lifetime
A $800 10 years
B $1,200 15 years

Pam expects to live in her new home for the foreseeable future, which means she will use the oven for at least 10 years. She wants to know which oven is the better value for her money.

To determine which oven is the better value, we need to calculate the daily cost of each option. We can do this by dividing the price of each oven by its expected lifetime.

Daily Cost of Oven A

The daily cost of Oven A is:

$80010 years=$800365×10=$8003650≈$0.22 per day\frac{\$800}{10 \text{ years}} = \frac{\$800}{365 \times 10} = \frac{\$800}{3650} \approx \$0.22 \text{ per day}

Daily Cost of Oven B

The daily cost of Oven B is:

$1,20015 years=$1,200365×15=$1,2005475≈$0.22 per day\frac{\$1,200}{15 \text{ years}} = \frac{\$1,200}{365 \times 15} = \frac{\$1,200}{5475} \approx \$0.22 \text{ per day}

As we can see, the daily costs of both ovens are approximately equal, at $0.22 per day. This means that, in terms of daily cost, both ovens are equally good options for Pam.

However, we need to consider the expected value of each oven. The expected value of an oven is the sum of its expected lifetime and its daily cost. We can calculate the expected value of each oven as follows:

Expected Value of Oven A

The expected value of Oven A is:

Expected Value=Expected Lifetime+Daily Cost×Expected Lifetime\text{Expected Value} = \text{Expected Lifetime} + \text{Daily Cost} \times \text{Expected Lifetime}

Expected Value of Oven A=10 years+$0.22 per day×365×10\text{Expected Value of Oven A} = 10 \text{ years} + \$0.22 \text{ per day} \times 365 \times 10

Expected Value of Oven A=10 years+$808≈$808+$0.22×3650\text{Expected Value of Oven A} = 10 \text{ years} + \$808 \approx \$808 + \$0.22 \times 3650

Expected Value of Oven A=$808+$808≈$1616\text{Expected Value of Oven A} = \$808 + \$808 \approx \$1616

Expected Value of Oven B

The expected value of Oven B is:

Expected Value of Oven B=15 years+$0.22 per day×365×15\text{Expected Value of Oven B} = 15 \text{ years} + \$0.22 \text{ per day} \times 365 \times 15

Expected Value of Oven B=15 years+$1080≈$1080+$0.22×5475\text{Expected Value of Oven B} = 15 \text{ years} + \$1080 \approx \$1080 + \$0.22 \times 5475

Expected Value of Oven B=$1080+$1200≈$2280\text{Expected Value of Oven B} = \$1080 + \$1200 \approx \$2280

As we can see, the expected value of Oven A is approximately $1616, while the expected value of Oven B is approximately $2280. This means that Oven B has a higher expected value than Oven A.

In conclusion, while both ovens have the same daily cost, Oven B has a higher expected value due to its longer expected lifetime. Therefore, based on the mathematical analysis, Oven B is the better value for Pam's money.

Based on the analysis, we recommend that Pam purchase Oven B. While it is more expensive upfront, its longer expected lifetime and higher expected value make it the better value in the long run.

This analysis assumes that the prices and expected lifetimes of the ovens are fixed and that Pam will use the oven for at least 10 years. In reality, there may be other factors to consider, such as the cost of maintenance and repairs, and the potential for technological advancements that may affect the ovens' performance. However, based on the information provided, Oven B is the better value for Pam's money.
Pam's Oven Purchase Decision: A Mathematical Analysis - Q&A

In our previous article, we analyzed the situation mathematically and provided Pam with a framework to make an informed decision about which oven to purchase. However, we understand that there may be many questions and concerns that Pam and other readers may have. In this article, we will address some of the most frequently asked questions and provide additional insights to help readers make a decision.

A: If you don't plan to use the oven for 10 years, the expected value analysis may not be as relevant. In this case, you may want to consider the upfront cost of each oven and compare them directly. However, keep in mind that the longer expected lifetime of Oven B may still make it a better value in the long run.

A: We did not include the cost of maintenance and repairs in our analysis, as this information was not provided. However, if you expect to incur significant costs for maintenance and repairs, you may want to factor these costs into your decision. In this case, Oven A may be a better option due to its lower upfront cost.

A: If you plan to upgrade to a new oven in the future, the expected value analysis may not be as relevant. In this case, you may want to consider the flexibility and upgrade options offered by each oven. Oven B may be a better option in this case, as it is a more modern and technologically advanced oven.

A: Yes, the expected value analysis can be used for other purchases, not just ovens. Anytime you are considering a purchase with a significant upfront cost and a long expected lifetime, the expected value analysis can be a useful tool to help you make a decision.

A: To calculate the expected value of other purchases, you will need to follow the same steps as we did in our analysis. First, determine the expected lifetime of the item. Then, calculate the daily cost of the item by dividing the upfront cost by the expected lifetime. Finally, multiply the daily cost by the expected lifetime to get the expected value.

A: If you have multiple options to choose from, you can use the expected value analysis to compare them directly. Simply calculate the expected value of each option and compare them to determine which one is the best value.

In conclusion, the expected value analysis can be a useful tool to help you make informed decisions about purchases with significant upfront costs and long expected lifetimes. By considering the expected value of each option, you can make a more informed decision and avoid costly mistakes.

Based on our analysis, we recommend that Pam purchase Oven B. While it is more expensive upfront, its longer expected lifetime and higher expected value make it the better value in the long run. However, we also recommend that readers consider their individual circumstances and needs before making a decision.

For more information on the expected value analysis and how to apply it to your own purchasing decisions, we recommend the following resources:

We hope this Q&A article has provided additional insights and helpful information to readers. If you have any further questions or concerns, please don't hesitate to contact us.