Final answer:
Initially, the best production method is Method 1 with a total cost of $9,000. If the cost of labor rises to $200/unit, Method 1 is still the most cost-effective but now costs $14,000.
Step-by-step explanation:
To determine the best production method, we need to calculate the total cost for each method given the costs of labor and capital. We'll use the fact that in the winter, hiring labor costs $100/unit and a unit of capital costs $400.
- Method 1: (50 units of labor × $100) + (10 units of capital × $400) = $5,000 + $4,000 = $9,000
- Method 2: (20 units of labor × $100) + (40 units of capital × $400) = $2,000 + $16,000 = $18,000
- Method 3: (10 units of labor × $100) + (70 units of capital × $400) = $1,000 + $28,000 = $29,000
Initially, Method 1 is the most cost-effective with a total cost of $9,000. However, if the cost of labor rises to $200/unit, the calculations change:
- Method 1: (50 units of labor × $200) + (10 units of capital × $400) = $10,000 + $4,000 = $14,000
- Method 2: (20 units of labor × $200) + (40 units of capital × $400) = $4,000 + $16,000 = $20,000
- Method 3: (10 units of labor × $200) + (70 units of capital × $400) = $2,000 + $28,000 = $30,000
When the cost of labor increases, Method 1 remains the most cost-effective, albeit more expensive than before at $14,000.