The local hospital’s emergency department has 6 trauma bays. On average, patients requiring a trauma bay arrive at the rate of 1 every 30 minutes. The coefficient of variation of inter-arrival time is 1. If the hospital has an available trauma bay, it is immediately allocated to a needy patient. If there are no trauma bays available, the patient is sent to another hospital. On average, a patient’s length of stay in a trauma bay is 1.5 hours (with a standard deviation of 1.5 hours). The hospital’s emergency department operates 24 hours a day.
1) How many patients are treated in the trauma bays of this hospital on an average 24 hour day?
2) When a patient is diverted to another hospital, the diverting hospital has to pay for the expenditure incurred to guarantee the patient’s life, which costs the hospital $200 per diverted patient. What is the average daily cost (in $) for the hospital from patients that are being diverted to other hospitals?