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Question: On average, 5 patients per hour come to the clinic (Poisson). The average time to serve a patient is 27 minutes (exponential). The clinic has 2 doctors. When its waiting room is full (15 places), the clinic directs new patients to the emergency room.
a) calculate the arrival rate, service rate, # of servers and queue capacity.
b) We want to reduce the average time spent in the waiting room to less than 40 minutes. 3 possibilities:1- reduce the average service time to 20 minutes per patient by hiring a nurse practitioner ($100/hour)2- reduce the size of the waiting room. $10 per place collected.3- add a doctor ($200/hour)In addition, the clinic suffers a loss of opportunity of $200 for each patient redirected to the emergency room.
Repeat the calculations in a) and calculate the total cost of each option. Based on costs, which option do you recommend?
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