Final answer:
The best production method is Method 1 both initially and after the cost of labor rises since it has the lowest total cost in both scenarios.
Step-by-step explanation:
To determine the best production method, we need to calculate the total cost of each method based on the cost of labor and capital.
Original Labor Cost at $100/unit:
- Method 1: Total Cost = (50 units of labor × $100/unit) + (10 units of capital × $400/unit) = $5000 + $4000 = $9000
- Method 2: Total Cost = (20 units of labor × $100/unit) + (40 units of capital × $400/unit) = $2000 + $16000 = $18000
- Method 3: Total Cost = (10 units of labor × $100/unit) + (70 units of capital × $400/unit) = $1000 + $28000 = $29000
The company should use Method 1 as it has the lowest total cost.
Increased Labor Cost at $200/unit:
- Method 1: Total Cost = (50 units of labor × $200/unit) + (10 units of capital × $400/unit) = $10000 + $4000 = $14000
- Method 2: Total Cost = (20 units of labor × $200/unit) + (40 units of capital × $400/unit) = $4000 + $16000 = $20000
- Method 3: Total Cost = (10 units of labor × $200/unit) + (70 units of capital × $400/unit) = $2000 + $28000 = $30000
Even with the cost of labor rising, Method 1 remains the most cost-effective production method.