Final answer:
When the cost of labor remains at $40 and the cost of machines decreases to $50, Technology 3 with a total cost of $170 is the most cost-effective production method for the firm.
Step-by-step explanation:
The student's question refers to the allocation of overhead costs and the changes in costs when production processes are altered. In this scenario, we are given the overhead costs and the change in hours due to automation. With the cost of labor constant at $40 and the cost of a machine reducing to $50, we need to calculate the new total costs for each production method and determine which would be the optimal method for the firm to use.
For Technology 1, with 10 hours of labor, the total cost would be (10 × $40) + (1 × $50) = $450.
For Technology 2, with 7 hours of labor, the total cost would be (7 × $40) + (1 × $50) = $330.
For Technology 3, with 3 hours of labor, the total cost would be (3 × $40) + (1 × $50) = $170.
The firm should use the method with the lowest total cost, which is Technology 3, as it provides the lowest cost of $170, combining low labor hours with the decreased cost of machine usage. This is advantageous especially if the firm wants to minimize labor costs and leverage the lower cost of machinery.