Final answer:
The best production method initially 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.
Step-by-step explanation:
The question asks for the best production method considering the costs of labor and capital using three different production methods. Initially, labor costs $100/unit, and capital costs $400/unit. To determine which method is the most cost-effective initially, we can calculate the total costs for each method:
- 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
Therefore, the best production method initially is Method 1 with the lowest cost of $9,000.
If the cost of labor rises to $200/unit, we recalculate:
- 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
With the increased labor cost, Method 1 remains the best production method at a cost of $14,000.