One freezer costs 723.95 and uses 90 kilowatt hours ( kwh ) of electricity each month. A second

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One freezer costs 723.95 and uses 90 kilowatt hours ( kwh )...

One freezer costs $\$ 723.95$ and uses 90 kilowatt hours ( $\mathrm{kwh}$ ) of electricity each month. A second freezer costs $\$ 600$ and uses $100 \mathrm{kwh}$ of electricity each month. The expected life of each freezer is 12 years. What is the minimum electric rate (in cents per kwh) for which the 12-year total cost (purchase price + electricity costs) will be less for the first freezer?

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Key Concepts

Break-even Analysis

Break-even analysis is the process of determining the point at which two options have equal total costs. It involves finding the critical value (such as a price per unit) where the sum of initial investment and ongoing expenses for one option becomes lower or higher than the alternative, thus indicating when one choice is more cost-effective over time.

Life Cycle Cost Analysis

Life cycle cost analysis evaluates the total cost of an asset over its entire lifespan, including the initial purchase price and all subsequent operating costs. In many decision-making scenarios, comparing the long-term costs rather than just the upfront cost provides a clearer picture of the financial impact and helps in choosing the most economical option.

Energy Consumption and Cost Calculation

This concept involves calculating expenses based on the energy consumption of a device or system. It requires determining the total energy used over a period and multiplying it by the rate per kilowatt-hour. This calculation is essential when comparing the operational costs of appliances or systems with different energy usages.

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