Final answer:
The best production method for the company can be determined by comparing the total costs of each method. Method 1, with 50 units of labor and 10 units of capital, has the lowest total cost. Even if the cost of labor rises, Method 1 will still have the lowest total cost.
Step-by-step explanation:
The best production method can be determined by comparing the total cost of each method. Let's calculate the total cost for each method:
Method 1: 50 units of labor * $100/unit + 10 units of capital * $400 = $5,000 + $4,000 = $9,000
Method 2: 20 units of labor * $100/unit + 40 units of capital * $400 = $2,000 + $16,000 = $18,000
Method 3: 10 units of labor * $100/unit + 70 units of capital * $400 = $1,000 + $28,000 = $29,000
Based on these calculations, the company should use Method 1 as it has the lowest total cost. If the cost of labor rises to $200/unit, the new total costs for each method would be:
Method 1: 50 units of labor * $200/unit + 10 units of capital * $400 = $10,000 + $4,000 = $14,000
Method 2: 20 units of labor * $200/unit + 40 units of capital * $400 = $4,000 + $16,000 = $20,000
Method 3: 10 units of labor * $200/unit + 70 units of capital * $400 = $2,000 + $28,000 = $30,000
Even with the increased cost of labor, Method 1 still has the lowest total cost and would remain the best production method for the company.