Final answer:
The answer to the question is (a) service cost increases and waiting cost decreases when the number of servers in a waiting line system increases. This balance reflects the trade-off between the resources required to provide the service and the benefits of reduced customer waiting times.
Step-by-step explanation:
When considering the question of how the number of servers in a waiting line system affects service cost and waiting cost, we must understand the balance between these two types of costs. As we increase the number of servers, there is an immediate impact on costs – increasing the number of servers typically leads to a higher overall service cost because more resources are required to pay for labor and possibly equipment. However, this increase in service capacity usually results in reduced waiting times for customers, thereby decreasing the waiting cost which could include lost customer goodwill and potential sales.
Thus, the correct option in this scenario would be option (a): service cost increases and waiting cost decreases. Applying this to specific examples like Figure 8.8 Adjustment Process in a Constant-Cost Industry, the situation mirrors a supply and demand scenario where the introduction of more servers is analogous to an increase in supply. If we consider a scenario like a technological improvement that reduces production costs, a similar balance occurs where initial profits attract new firms until equilibrium is restored.
Also, when discussing things like the arrival of customers in a store, we see that these dynamics can apply to customer flow and the capacity to serve them efficiently. For instance, if on average one customer arrives every two minutes, it would take six minutes on average for three customers to arrive. This illustrates the interplay of service capacity with arrival rates and corresponding waiting times.