An administrator in a small suburban hospital is concerned with the waiting lines in the emergency room, which is always staffed by at least one doctor. Patients arrive on average at the rate of 14 per hour. They are served on a first-come, first-served, basis. On average, one doctor, working alone, can treat a patient in 5 minutes. For each additional doctor added, 2 more patients can be seen in a hour by all doctors working together, on average. (Assume the Poisson arrivals and exponential service times) The administrator has set the objective that, on average, there should not be more than 6 patients waiting to see a doctor.

1. What is the minimum number of doctors needed to meet the administrator's objective?

(With the minimum number of doctors working all together)

a. How long does a patient have to wait to get seen by a doctor?

b. On average, how many patients are in the waiting room?

c. How many patients can be seen in an 8 hour work day?

d. How long will it take on average for a patient to be treated, from the time they arrive until the time they leave?