Switching from the strategic stockpiling decision of ventilators before a pandemic, we now examine the operational level decisions by a hospital operating ventilator during the pandemic. During the COVID-19 crisis, many hospitals have run short of ventilators while other facilities scramble to prepare for the coming demand surge. A local hospital in Toronto is planning for the next wave of COVID-19. From the data, it is estimated that the average length of stay on a ventilator for a non-COVID-19 patient is 4 days, and the average length of stay on a ventilator for a COVID-19 patient is 12 days. It is expected that during the next wave, there will be an average of 2.7 new non-COVID-19 patients arriving at the hospital per day who need to be put on ventilators and an average of 4.5 new COVID-19 patients arriving per day who need to be put on ventilators. The latter estimate on the new COVID-19 patients for ventilators is based on an estimated 100 new cases each day arriving at the hospital in the next wave, as 4.5% of those severe cases arriving at the hospital are expected to be put on ventilators. The check-in time of patients is independent, one from another. It is safe to assume that the length of stay across the mix of incoming COVID-19 and non-COVID-19 patients has a standard deviation of 4.5 days. The hospital currently has 67 ventilators.

1. What is the arrival rate to the ventilators' system in terms of the number of patients per day?

2. What is the CVa in the arrivals to this system?

3. What is the service rate of each ventilator, in terms of the number of "average" patients per day? Use 4 decimal places.

4. What is CVp in the length of stay across the expected mix of incoming COVID-19 and non-COVID-19 patients?

5. What is the current average wait time (in hours) of patients before they are put on ventilators?

6. What is the probability that a new patient has to wait, without being immediately put on a ventilator? Use three decimal places.

7. Assuming the hospital runs nonstop around the clock. To ensure that patients wait only about2 hours on average, how many more ventilators would the hospital need to get from the government in addition to what it currently has?

8. If the hospital estimates that each respiratory therapist (RT), who is trained to operate ventilators, cannot supervise more than 4 ventilators simultaneously, how many RTs does the hospital need to staff to meet the above 2-hour average wait goal?

9. Assuming this 2-hour average wait target is just met, what is the probability that the actual wait for a ventilator is more than 4 hours?