Final answer:
Initially, Method 1 is the best production method with a total cost of $9,000. Even when labor costs rise to $200/unit, Method 1 remains the most cost-effective with a new total of $14,000.
Step-by-step explanation:
To determine the best production method, we must calculate the total costs for each method using the given costs for labor and capital. We then compare these costs to decide on the optimal method. A change in labor costs will affect this decision since it directly influences the total cost of each production method.
Initial Cost Calculation
For Method 1: (50 units of labor × $100/unit) + (10 units of capital × $400/unit) = $9,000.
For Method 2: (20 units of labor × $100/unit) + (40 units of capital × $400/unit) = $18,000.
For Method 3: (10 units of labor × $100/unit) + (70 units of capital × $400/unit) = $29,000.
Thus, Method 1 is the cheapest with initial labor costs.
Adjusted Cost Calculation With Increased Labor Costs
For Method 1: (50 units of labor × $200/unit) + (10 units of capital × $400/unit) = $14,000.
For Method 2: (20 units of labor × $200/unit) + (40 units of capital × $400/unit) = $18,000.
For Method 3: (10 units of labor × $200/unit) + (70 units of capital × $400/unit) = $29,000.
With increased labor costs, Method 1 still remains the least expensive and thus the best option.