please answer part c) how many doctors are required to reduce the average patient waiting time to below 1 minute?

26. Patients arrive at a clinic with inter-arrival times that have an average and standard deviation equal to 8.33 and 4.17 minutes, respectively. The clinic has 4 doctors and the service time of each doctor has mean and standard deviation equal to 24 and 14 minutes, respectively. Patients form one line to go into any of the 4 doctor's offices. a) What is the coefficient of variation of the inter-arrival times? (4 pts) b) What is the average number of patients in the waiting room? ( 5pts ) c) How many doctors are required to reduce the average patient waiting time to below 1 minute? (5 pts) Solution: a) By definition, CA=E(A)A=8.334.17=0.5006 b) A doctor's utilization is ==:42460cust/hr7.2cust/hr=0.7203. Average number in service is equal to c==40.7203. c) With c=4 servers, we can use PK formula to obtain, Lq=0.3742. Then, Wq=Lq=3.12 minutes. Repeating the same calculation for c=4, we have Wq=Lq=0.86 minutes