Final answer:
a. units of production method. The best production method based on 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 at $14000.
Step-by-step explanation:
When analyzing the best production method based on cost-efficiency, we need to calculate the total cost for each method provided. Currently, labor costs $100/unit and capital costs $400/unit.
Method 1 requires 50 units of labor and 10 units of capital. The total cost will be (50*$100) + (10*$400) = $5000 + $4000 = $9000.
Method 2 requires 20 units of labor and 40 units of capital. The total cost is (20*$100) + (40*$400) = $2000 + $16000 = $18000.
Method 3 requires 10 units of labor and 70 units of capital. The total cost is (10*$100) + (70*$400) = $1000 + $28000 = $29000.
With the current costs, Method 1 is the most cost-effective. If the cost of labor rises to $200/unit, the costs for each method are:
- Method 1: (50*$200) + (10*$400) = $10000 + $4000 = $14000
- Method 2: (20*$200) + (40*$400) = $4000 + $16000 = $20000
- Method 3: (10*$200) + (70*$400) = $2000 + $28000 = $30000
Even with the increased labor costs, Method 1 still remains the cheapest option.