Final answer:
The best production method based on costs is Method 1, both when labor is $100/unit and when labor cost increases to $200/unit. This method remains the most cost-effective in both scenarios.
Step-by-step explanation:
When assessing the best production method, one must consider the cost of labor and capital. Initially, labor costs $100 per unit, and capital costs $400 per unit. The total costs for each method are calculated as follows:
Method 1: (50 units of labor × $100) + (10 units of capital × $400) = $5000 + $4000 = $9000
Method 2: (20 units of labor × $100) + (40 units of capital × $400) = $2000 + $16000 = $18000
Method 3: (10 units of labor × $100) + (70 units of capital × $400) = $1000 + $28000 = $29000
Therefore, Method 1 is the most cost-effective with the initial labor and capital costs.
When the cost of labor rises to $200 per unit, the total costs are recalculated:
Method 1: (50 units of labor × $200) + (10 units of capital × $400) = $10000 + $4000 = $14000
Method 2: (20 units of labor × $200) + (40 units of capital × $400) = $4000 + $16000 = $20000
Method 3: (10 units of labor × $200) + (70 units of capital × $400) = $2000 + $28000 = $30000
With the increased labor cost, Method 1 remains the most cost-effective production method.