Final answer:
The best production method based on the given costs 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 choice with a new total cost of $14,000.
Step-by-step explanation:
To find the best production method based on the given costs of labor and capital, we must calculate the total cost for each method and then compare them.
For Method 1: (50 units of labor × $100/unit) + (10 units of capital × $400/unit) = $5,000 + $4,000 = $9,000
For Method 2: (20 units of labor × $100/unit) + (40 units of capital × $400/unit) = $2,000 + $16,000 = $18,000
For Method 3: (10 units of labor × $100/unit) + (70 units of capital × $400/unit) = $1,000 + $28,000 = $29,000.
Therefore, the best production method with the initial cost of labor is Method 1 with the lowest total cost of $9,000.
If the cost of labor rises to $200/unit, the calculations change.
For Method 1: (50 units of labor × $200/unit) + (10 units of capital × $400/unit) = $10,000 + $4,000 = $14,000
For Method 2: (20 units of labor × $200/unit) + (40 units of capital × $400/unit) = $4,000 + $16,000 = $20,000
For Method 3: (10 units of labor × $200/unit) + (70 units of capital × $400/unit) = $2,000 + $28,000 = $30,000.
When the cost of labor increases, Method 1 still remains the most cost-effective method with a new total cost of $14,000.