please answer and show work

SA 26 points 126 points] Consider a health clinic that has 12 doctors at any time. Currently, the arrival rate for each doctor is 3 patients per hour and it takes 18 minutes to serve each patient Both inter arrival times and service times have a coefficient of variation that is equal to one. Initially, each doctor serves her or his own patients a) (8 points What is the average number of customers waiting to see each doctor? What is the total average number of patients waiting to see a doctor? Hint: You have 12 doctors and so 12 separate lines with the same average number of patients. The clinic decides to change its process by converting to a pooled queue where the first available doctor sees the patient first in line. Assume the arrival and service times remain the same b) 8 poines After pooling, what is the average number of customers waiting to see a doctor? Compare your answer here to the total number of patients waiting to see a doctor in purta) and explain why it is smaller, equal or larger to points Suppose now that the standard deviation of the service time is changed to 12 minutes while all else remains the same as before and the queue is still pooled as in part b). What is the average number of patients waiting to see a doctor now? Compare your answer to part b) and explain why it is smaller, equal or larger di 14 points Suppose again that the standard deviation of the service time is changed to 12 minutes while all else remains the same as before and the queue is still pooled as in part b). Is the average number of patients being seen by a doctor smaller, equal or larger than the average number of patients being seen by a doctor in part b? No need to do math just explain your reasoning SA 26 points 126 points] Consider a health clinic that has 12 doctors at any time. Currently, the arrival rate for each doctor is 3 patients per hour and it takes 18 minutes to serve each patient Both inter arrival times and service times have a coefficient of variation that is equal to one. Initially, each doctor serves her or his own patients a) (8 points What is the average number of customers waiting to see each doctor? What is the total average number of patients waiting to see a doctor? Hint: You have 12 doctors and so 12 separate lines with the same average number of patients. The clinic decides to change its process by converting to a pooled queue where the first available doctor sees the patient first in line. Assume the arrival and service times remain the same b) 8 poines After pooling, what is the average number of customers waiting to see a doctor? Compare your answer here to the total number of patients waiting to see a doctor in purta) and explain why it is smaller, equal or larger to points Suppose now that the standard deviation of the service time is changed to 12 minutes while all else remains the same as before and the queue is still pooled as in part b). What is the average number of patients waiting to see a doctor now? Compare your answer to part b) and explain why it is smaller, equal or larger di 14 points Suppose again that the standard deviation of the service time is changed to 12 minutes while all else remains the same as before and the queue is still pooled as in part b). Is the average number of patients being seen by a doctor smaller, equal or larger than the average number of patients being seen by a doctor in part b? No need to do math just explain your reasoning