The manager of a bank wants to use an M/M/s queueing model to weigh the costs of extra tellers against the cost of having customers wait in line. The arrival rate is 60 customers per hour, and the average service time is four minutes. The cost of each teller is easy to gauge at the $11.50 per hour wage rate. However, because estimating the cost per minute of waiting time is difficult, the bank manager decides to hire the minimum number of tellers so that a typical customer has probability 0.05 of waiting more than five minutes in line.

a. How many tellers will the manager use, given this criterion?

b. By deciding on this many tellers as “optimal,” the manager is implicitly using some value (or some range of values) for the cost per minute of waiting time. That is, a certain cost (or cost range) would lead to the same number of tellers as suggested in part a. What is this implied cost (or cost range)?