Final answer:
To determine the maximum number of units that can be produced, analyze different production technologies and their associated labor and capital costs. Calculate the total costs for each method, assess the economies of scale, and decide on the least costly method to find the best production strategy. Adjust this analysis if input costs, like labor, change.
Step-by-step explanation:
How to Determine the Maximum Number of Units that Can Be Produced
To determine the maximum number of units that can be produced, you need to consider the production technologies available and the cost of input factors such as labor and capital. By comparing different production technologies, you can find the least costly option. For instance, if technology 1 requires 10 workers and 2 machines, technology 2 requires only 7 workers, and technology 3's requirements are not specified, you would compare the costs associated with these inputs.
If the cost of labor is initially $100 per unit and the cost of capital is $400 per unit, you would calculate the total cost for each method: Method 1 would cost (50 units of labor × $100) + (10 units of capital × $400), Method 2 and Method 3 would be calculated similarly. Once you have the costs for all methods, you can compare them to find the least costly production technology.
After determining this, you would then consider the optimal scale of production in relation to economies of scale. The optimal scale is where the cost per unit goes down as the quantity of output increases. You would have to assess the profit-maximizing output level, which in this case is output quantity 5 with profits of $40, and relate this to your production capacity and cost analysis.
If labor costs rise to $200 per unit, you would have to re-calculate the total costs for each production method. The method with the lowest total cost would then dictate the best production method.