Final answer:
The best production method based on cost is Method 1 with an initial cost of $9,000. From the provided methods, even when the labor cost increases to $200/unit, Method 1 remains the most cost-effective option with a new total cost of $14,000.
Step-by-step explanation:
To determine the best production method based on cost, we need to calculate the total cost for each method using the given costs of labor and capital. Initially, labor costs $100/unit and capital costs $400/unit. Consequently, the total costs for each method are as follows:
- Method 1: (50 units of labor × $100/unit) + (10 units of capital × $400/unit) = $9,000
- Method 2: (20 units of labor × $100/unit) + (40 units of capital × $400/unit) = $18,000
- Method 3: (10 units of labor × $100/unit) + (70 units of capital × $400/unit) = $29,000
Method 1 has the lowest total cost and is therefore the best production method initially. If the cost of labor rises to $200/unit, the new total costs will be:
- Method 1: (50 units of labor × $200/unit) + (10 units of capital × $400/unit) = $14,000
- Method 2: (20 units of labor × $200/unit) + (40 units of capital × $400/unit) = $18,000
- Method 3: (10 units of labor × $200/unit) + (70 units of capital × $400/unit) = $29,000
Even after the increase in the cost of labor, Method 1 remains the most cost-effective production method.