Final answer:
The goal in using a waiting line model to determine the number of technicians needed for machine maintenance is to minimize the total cost, including both maintenance and downtime costs (option a). This often involves choosing the production technology that offers the lowest total cost, which can vary depending on the cost of labor and machines.
Step-by-step explanation:
When analyzing the number of service technicians required to maintain machines in a factory using a waiting line model, our goal should be to minimize the total cost, which includes both the cost of maintenance and the cost of downtime. Choosing the right production technology is crucial in this process. For example, if machine hours become cheaper, a shift towards using more machines and less labor, such as opting for production technology 3, might be beneficial as it offers the lowest total cost.
However, if the cost of machines increases, like in the 1970s in the United States, there would likely be a shift towards less capital-intensive technology and more labor, indicating a preference for production technology 2, again based on its lower total cost. This careful balance helps prevent overstaffing, which increases maintenance costs, and understaffing, which increases machine downtime and reduces overall productivity.