Final answer:
To minimize costs, Method 1 should be used when labor costs $100/unit, as well as when labor costs rise to $200/unit. Economies of scale indicate that production costs are minimized at an output level of 150 units.
Step-by-step explanation:
To minimize cost and determine how many units should be produced, we need to consider the cost of labor and capital for each production method. Initially, hiring labor costs $100/unit and a unit of capital costs $400. Calculating the total cost for each method, we have:
- Method 1: (50 units of labor × $100) + (10 units of capital × $400) = $9000
- Method 2: (20 units of labor × $100) + (40 units of capital × $400) = $18000
- Method 3: (10 units of labor × $100) + (70 units of capital × $400) = $29000
Therefore, Method 1 minimizes costs initially. If the cost of labor rises to $200 per unit, the new costs are:
- Method 1: (50 units of labor × $200) + (10 units of capital × $400) = $13000
- Method 2: (20 units of labor × $200) + (40 units of capital × $400) = $18000
- Method 3: (10 units of labor × $200) + (70 units of capital × $400) = $29000
With the increased labor cost, Method 1 still remains the method that minimizes costs.
Regarding economies of scale, looking at the given information on production plants, we understand that there is a cost advantage in producing more units. Specifically, production plants L and V can produce at a lower cost per unit than S or M when production is up to 150 units. Above this output level, there's no further cost advantage. Therefore, the cost will be minimized at an output level of 150 units based on the available data.