Final answer:
The best production method given the cost of labor at $100/unit and capital at $400/unit is Method 1, with a total cost of $9000. If the cost of labor increases to $200/unit, Method 1 remains the most cost-effective option with a new total cost of $14000.
Step-by-step explanation:
To determine the best production method based on cost we need to calculate the total cost for each method. We are given the cost of labor, which is $100/unit, and the cost of capital, which is $400/unit. Using these figures, we can calculate:
- 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
Therefore, the best production method initially is Method 1, with the lowest total cost of $9000.
If the cost of labor rises to $200/unit, then we need to recalculate:
- 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
With the increased labor cost, Method 1 still remains the most cost-effective. It's essential for the company to continuously evaluate changes in labor and capital costs to maintain cost efficiency.