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). 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 one hour (with a standard deviation of 1.5 hours). The hospital’s emergency department operates 24 hours a day.
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 $250 per patient sent. What is the average daily cost (in $) for the hospital from patients that are being sent to other hospitals?