Consider a single-line, single-server waiting line system. Suppose there is only physical space for 4 people in the system. That is, one being served and 3 in line. The arrival rate is 75 people per hour. The manager, Tim S., wants to save money by hiring the slowest worker he can and at the same time, keep the average number of people in the system at 4.

1. Using Tim's strategy, what must the service rate per hour be? You must show your calculations.
2. What is the probability of having 5 of more people in the system and therefore running out of room? Again, you must show your calculations.
3. Even if Tim S. does all the math correctly, he has not accounted for one key factor. What has he ignored and why is that factor so important?