Final answer:
The best production method when labor costs $100/unit is Method 1 with a total cost of $9,000. If the cost of labor increases to $200/unit, Method 1 remains the most cost-effective with a total cost of $14,000.
Step-by-step explanation:
To determine the best production method based on the costs provided, we need to calculate the total cost for each method using the cost per unit of labor ($100/unit for the winter scenario and $200/unit for the increased labor cost scenario) and the cost per unit of capital ($400/unit).
For the initial scenario with labor costing $100/unit:
Method 1: (50 units of labor x $100) + (10 units of capital x $400) = $5,000 + $4,000 = $9,000
Method 2: (20 units of labor x $100) + (40 units of capital x $400) = $2,000 + $16,000 = $18,000
Method 3: (10 units of labor x $100) + (70 units of capital x $400) = $1,000 + $28,000 = $29,000
For the scenario where the cost of labor rises to $200/unit:
Method 1: (50 units of labor x $200) + (10 units of capital x $400) = $10,000 + $4,000 = $14,000
Method 2: (20 units of labor x $200) + (40 units of capital x $400) = $4,000 + $16,000 = $20,000
Method 3: (10 units of labor x $200) + (70 units of capital x $400) = $2,000 + $28,000 = $30,000
The best production method when labor is $100/unit is Method 1, with the lowest total cost of $9,000. If the cost of labor rises to $200/unit, Method 1 still remains the most cost-effective with a total cost of $14,000.