Final answer:
The best production method when labor costs $100/unit and capital costs $400/unit is Method 1, with a total cost of $9,000. If the cost of labor increases to $200/unit, Method 1 is still the most cost-effective option, with a new total cost of $14,000.
Step-by-step explanation:
To determine the best production method when hiring labor costs $100/unit and capital costs $400/unit, we must calculate the total cost for each method:
- Method 1: Cost = (50 units of labor × $100/unit) + (10 units of capital × $400/unit) = $5,000 + $4,000 = $9,000
- Method 2: Cost = (20 units of labor × $100/unit) + (40 units of capital × $400/unit) = $2,000 + $16,000 = $18,000
- Method 3: Cost = (10 units of labor × $100/unit) + (70 units of capital × $400/unit) = $1,000 + $28,000 = $29,000
Using these calculations, we can see the Method 1 is the most cost-efficient.
If the cost of labor increases to $200/unit, we need to recalculate:
- Method 1: Cost = (50 units of labor × $200/unit) + (10 units of capital × $400/unit) = $10,000 + $4,000 = $14,000
- Method 2: Cost = (20 units of labor × $200/unit) + (40 units of capital × $400/unit) = $4,000 + $16,000 = $20,000
- Method 3: Cost = (10 units of labor × $200/unit) + (70 units of capital × $400/unit) = $2,000 + $28,000 = $30,000
With the increased cost of labor, Method 1 remains the most cost-effective.