Final answer:
The best production method when labor costs $100/unit and capital $400/unit is Method 1 with a total cost of $9000. If the cost of labor rises to $200/unit, Method 1 is still the best option at $14000. When labor costs $40/unit and capital falls to $50/unit, Method 1 again has the lowest cost of $2500.
Step-by-step explanation:
The question asks about determining the best production method based on the costs of labor and capital for different methods. When labor cost is $100/unit and capital cost is $400/unit, we calculate the total cost for each method:
- Method 1: (50 units of labor × $100/unit) + (10 units of capital × $400/unit) = $9000
- Method 2: (20 units of labor × $100/unit) + (40 units of capital × $400/unit) = $18000
- Method 3: (10 units of labor × $100/unit) + (70 units of capital × $400/unit) = $29000
Method 1 is the best choice with the lowest cost of $9000. However, if labor cost rises to $200/unit, the calculations change:
- Method 1: (50 units of labor × $200/unit) + (10 units of capital × $400/unit) = $14000
- Method 2: (20 units of labor × $200/unit) + (40 units of capital × $400/unit) = $18000
- Method 3: (10 units of labor × $200/unit) + (70 units of capital × $400/unit) = $29000
With the increased labor cost, Method 1 remains the best option at $14000, still being the cheapest. In the case where labor cost is $40/unit and capital cost decreases to $50/unit, we would recalculate:
- Method 1: (50 units of labor × $40/unit) + (10 units of capital × $50/unit) = $2500
- Method 2: (20 units of labor × $40/unit) + (40 units of capital × $50/unit) = $3000
- Method 3: (10 units of labor × $40/unit) + (70 units of capital × $50/unit) = $4000
With the decreased cost of capital, Method 1 still offers the lowest total cost at $2500 and should be the method chosen by the firm.