Please show all work and math for each part.

4. (10 points) A hospital emergency room (ER) is currently organized so that all patients register through an initial check-in-process. At his or her turn, each patient is seen by a doctor and then exits the process, either with a prescription or with admission to the hospital. Currently, 40 people per hour arrive at the ER, 20% of these individuals are admitted to the hospital. On average 8 people are waiting to be registered and 16 are registered and waiting to see a doctor. The registration process takes, on average, 3 minutes per patient. Among patients who receive prescriptions, average time spent with a doctor is 15 minutes. Among those admitted to the hospital, average time is 45 minutes. The flowchart for this process is shown below. Potential admits 20% Arrival rate- 40 Patients/hr Registration Doctor 3 min./ patient Buffer 1 Buffer 2 Admit 45 min. 80% Prescription 15 min. Simple Prescription Assuming the process is stable (ie, average arrival rate equals average throughput rate), answer The following questions. You will need to use Little's Law. a. What is the average amount of time (in minutes) spent in Buffer 1 by a patient? b. On average, how many patients are at the registration desk being served? c. On average, how many potential admits are being examined by doctors? HINT: Arrival rates are different for potential admits and simple prescription. d. On average, how many simple prescription are being examined by doctors? e. On average, how many patients are in the ER (.e., the entire system shown above)? Location WIP Buffer 1 Registration Buffer 2 Doctor (Potential Admits) Doctor (Prescription Only) Total