I know this is a long question! If you are able to answer it, post in the comments and I will create an additional posting for each part (a, b, c, d,e ) so you can get credit for 4 answers.

Following the ER system in the Chicago Hospital, a consulting team recommends a Triage system. Under the triage system, the patients register as before. But after registration, they will be quickly examined by a nurse practitioner. The nurse practitioner will classify them first as 'Prescription' or 'Admission.' The 'Prescription' patients will move to a regular care area and 'Admission' will be taken to 'emergency' area. The estimated nurse examination time will take 3 minutes in average, they expect that, on average, 1.3 patients will be waiting to register and 0.8 patient will be waiting for the triage nurse. The consultant estimates that the "prescription' area will have, on average, 1.7 patients waiting to be seen by a doctor (assume that the doctor's time takes 5 minutes now). The consultant also estimates that the 'Admission' area will have 1.2 patients waiting for the doctor, and each patient will take 25 minutes with the doctor now. Assume that 4 patients will be admitted to the hospital and the triage nurse is 100% accurate in his/her assessment and classification. (A) How long, on average, will a patient spend in the ER system under the new proposed triage system? (B) How long, on average, will a 'prescription' patient spend in the ER? (C) On average, how many patients are being examined by doctors? (D) On average, how many patients will be in the ER (E) How does the new Triage change the system's performance? Is it getting better or worse? (It may not be simple black & white) Following the ER system in the Chicago Hospital, a consulting team recommends a Triage system. Under the triage system, the patients register as before. But after registration, they will be quickly examined by a nurse practitioner. The nurse practitioner will classify them first as 'Prescription' or 'Admission.' The 'Prescription' patients will move to a regular care area and 'Admission' will be taken to 'emergency' area. The estimated nurse examination time will take 3 minutes in average, they expect that, on average, 1.3 patients will be waiting to register and 0.8 patient will be waiting for the triage nurse. The consultant estimates that the "prescription' area will have, on average, 1.7 patients waiting to be seen by a doctor (assume that the doctor's time takes 5 minutes now). The consultant also estimates that the 'Admission' area will have 1.2 patients waiting for the doctor, and each patient will take 25 minutes with the doctor now. Assume that 4 patients will be admitted to the hospital and the triage nurse is 100% accurate in his/her assessment and classification. (A) How long, on average, will a patient spend in the ER system under the new proposed triage system? (B) How long, on average, will a 'prescription' patient spend in the ER? (C) On average, how many patients are being examined by doctors? (D) On average, how many patients will be in the ER (E) How does the new Triage change the system's performance? Is it getting better or worse? (It may not be simple black & white)