Final answer:
The best production method based on the given costs is Method 1, both when labor costs $100/unit and when it increases to $200/unit, as it results in the lowest total cost.
Step-by-step explanation:
The question at hand is concerned with identifying the best production method based on the costs of labor and capital. We have three methods to compare, each with different requirements of labor and capital:
- Method 1: 50 units of labor, 10 units of capital
- Method 2: 20 units of labor, 40 units of capital
- Method 3: 10 units of labor, 70 units of capital
When labor costs $100/unit and capital costs $400/unit:
- Method 1 cost = (50 × $100) + (10 × $400) = $5,000 + $4,000 = $9,000
- Method 2 cost = (20 × $100) + (40 × $400) = $2,000 + $16,000 = $18,000
- Method 3 cost = (10 × $100) + (70 × $400) = $1,000 + $28,000 = $29,000
Method 1 is the most cost-effective at the initial labor cost.
If the cost of labor rises to $200/unit, the new costs are:
- Method 1 cost = (50 × $200) + (10 × $400) = $10,000 + $4,000 = $14,000
- Method 2 cost = (20 × $200) + (40 × $400) = $4,000 + $16,000 = $20,000
- Method 3 cost = (10 × $200) + (70 × $400) = $2,000 + $28,000 = $30,000
At the higher labor cost, Method 1 remains the most cost-effective.