The local pediatric office here in Bloomington operates a walk-in clinic with special hours, and the office needs to know how many nurses to staff. (It is ok to have non-integer values of patients in this problem.) During business hours (9a to 5p), nurses receive a pay rate of $20 per hour, but they work as one team. Thus, if one nurse is hired, he or she works alone; two or three people work together on the same patient case. For the patients who are seen during business hours, one nurse can treat a patient in an average time of 30 minutes. Two nurses take 20 minutes, and three take 15 minutes. While patients are in the clinic, the clinic must pay the local township for access to parking spaces, and the cost for each patient is $30 per hour. Assume exponential arrivals and exponential service rates for now. Under these conditions The clinic is considering shifting to seeing patients by appointment only during business hours (9a to 5p), but everything else stays the same. Under these conditions

1. What is the utilization percentage if the clinic hires one nurse?
2. What is the average time in the system (in minutes) if the clinic hires two nurses?
3. What is the average time in the system (in minutes) if the clinic hires three nurses?
4. What is the average number of patients in the system if the clinic hires two nurses?
5. What is the average number of patients in the system if the clinic hires three nurses?
6. How many nurses should the clinic hire?