Final answer:
The best production method based on the given cost of labor ($100/unit) and capital ($400/unit) is Method 1 with a total cost of $9,000. When the cost of labor increases to $200/unit, Method 1 is still the most cost-effective with a total cost of $14,000.
Step-by-step explanation:
A common way to allocate shared asset costs across business units is to allocate these costs based on several possible methods, such as revenue proportion, unit sales, number of employees, or direct labor hours. The choice of method can vary depending on the nature of the business and the relevance of each basis to the shared costs.
For the given example, we have three methods of production with different combinations of labor and capital. Calculating the total costs for each method under different labor costs scenarios will help us to determine the most cost-effective production method.
Using the costs of $100/unit for labor and $400/unit for capital:
- Method 1: (50 units of labor × $100) + (10 units of capital × $400) = $9,000
- Method 2: (20 units of labor × $100) + (40 units of capital × $400) = $17,000
- Method 3: (10 units of labor × $100) + (70 units of capital × $400) = $29,000
If the cost of labor rises to $200/unit:
- Method 1: (50 units of labor × $200) + (10 units of capital × $400) = $14,000
- Method 2: (20 units of labor × $200) + (40 units of capital × $400) = $18,000
- Method 3: (10 units of labor × $200) + (70 units of capital × $400) = $30,000
It is clear that Method 1 is the best production method when labor costs $100/unit. However, if the cost of labor doubles to $200/unit, Method 1 still remains the most cost-effective approach, despite the increase in labor costs, confirming that flexibility in production methods is important in response to changes in input costs.