Final answer:
The best production method based on the costs of labor and capital is Method 1, both before and after the rise in labor costs from $100/unit to $200/unit. It results in the lowest total production cost in both scenarios.
Step-by-step explanation:
In evaluating the best production method, the total costs associated with labor and capital must be considered. Initially, with labor costing $100/unit and capital costing $400/unit, the total cost for each method would be:
- Method 1: (50 units of labor * $100) + (10 units of capital * $400) = $5,000 + $4,000 = $9,000
- Method 2: (20 units of labor * $100) + (40 units of capital * $400) = $2,000 + $16,000 = $18,000
- Method 3: (10 units of labor * $100) + (70 units of capital * $400) = $1,000 + $28,000 = $29,000
Under these circumstances, Method 1 is the most cost-effective with a total production cost of $9,000.
If the cost of labor increases to $200/unit, the total costs will change as follows:
- Method 1: (50 units of labor * $200) + (10 units of capital * $400) = $10,000 + $4,000 = $14,000
- Method 2: (20 units of labor * $200) + (40 units of capital * $400) = $4,000 + $16,000 = $20,000
- Method 3: (10 units of labor * $200) + (70 units of capital * $400) = $2,000 + $28,000 = $30,000
Even with the rise in labor cost, Method 1 remains the cheapest option at $14,000. Therefore, Method 1 should be used irrespective of the change in labor cost.