Final answer:
The production level for maximum profit can be determined by comparing the total costs of different production methods. Initially, Method 1 is the most cost-effective, and remains so even when the cost of labor doubles, thus it represents the production level for the maximum profit.
Step-by-step explanation:
To find the production level for maximum profit, we need to consider the cost of both labor and capital. Initially, labor costs $100 per unit and capital costs $400 per unit. The total costs for each method would be as follows:
- Method 1: (50 units of labor × $100) + (10 units of capital × $400) = $9,000
- Method 2: (20 units of labor × $100) + (40 units of capital × $400) = $18,000
- Method 3: (10 units of labor × $100) + (70 units of capital × $400) = $29,000
Thus, the best production method based on the lowest cost is Method 1.
If the cost of labor rises to $200 per unit, the costs for each method would be:
- Method 1: (50 units of labor × $200) + (10 units of capital × $400) = $13,000
- Method 2: (20 units of labor × $200) + (40 units of capital × $400) = $18,000
- Method 3: (10 units of labor × $200) + (70 units of capital × $400) = $29,000
In this scenario, Method 1 still remains the most cost-effective production method.