Answer and Explanation:
To determine the more economical alternative and whether they are mutually exclusive or independent, we will use the present worth method and analyze the costs and savings for each alternative.
a) Present worth method:
To compare the alternatives using the present worth method, we need to calculate the present worth of costs and savings for each alternative. The alternative with the lower present worth of costs will be the more economical choice.
Let's calculate the present worth for each alternative using a minimum attractive rate of return (MARR) of 6% per year:
Alternative A:
Costs: $10,000
Savings per year: $2,500
To calculate the present worth, we need to discount the savings over the project's life. Let's assume the project's life is 5 years.
Present worth of costs for Alternative A: $10,000
Present worth of savings for Alternative A: $2,500 / (1 + 0.06)^1 + $2,500 / (1 + 0.06)^2 + $2,500 / (1 + 0.06)^3 + $2,500 / (1 + 0.06)^4 + $2,500 / (1 + 0.06)^5
Alternative B:
Costs: $7,500
Savings per year: $2,000
Present worth of costs for Alternative B: $7,500
Present worth of savings for Alternative B: $2,000 / (1 + 0.06)^1 + $2,000 / (1 + 0.06)^2 + $2,000 / (1 + 0.06)^3 + $2,000 / (1 + 0.06)^4 + $2,000 / (1 + 0.06)^5
Compare the present worth of costs for both alternatives. The alternative with the lower present worth of costs is the more economical choice.
b) Mutually exclusive or independent:
To determine whether the alternatives are mutually exclusive or independent, we need to consider whether selecting one alternative excludes the possibility of selecting the other.
If the alternatives are mutually exclusive, selecting one alternative means we cannot choose the other. In this case, the manufacturer must choose between Alternative A and Alternative B.
If the alternatives are independent, the manufacturer can select both alternatives simultaneously.
Based on the given information, it is not explicitly mentioned whether the alternatives are mutually exclusive or independent. Therefore, we cannot determine their relationship without further information or clarification from the manufacturer.
In summary, using the present worth method with a MARR of 6% per year, we can determine the more economical alternative by comparing the present worth of costs. However, without additional information, we cannot determine whether the alternatives are mutually exclusive or independent.