The local hospital's emergency department has 6 trauma bays. On average, patients requiring a trauma bay arrive every 30 minutes (with a coefficient of variation of 1, no seasonality exists). 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.

a What percentage of the patients requiring trauma bays end up being sent to another hospital?

b How many patients are treated in the trauma bays on an average 24 hour day?

c When a patient is sent to another hospital, the hospital has to put a staff with adequate skills to guarantee the patient's life, which costs the hospital $200 per patient sent. What is the average daily cost for the hospital from patients that are being sent to other hospitals?

d New state regulations require that every emergency department be able to accommodate at least 90% of all patients needing a trauma bay with no waiting. What is the minimum number of trauma bays necessary to meet this requirement? (Assume that the time spent in the trauma bay cannot be changed)