You have recently accepted a process improvement job for a regional healthcare system. System administrators are concerned about the waiting times at a small local hospital emergency room and have charged you with analyzing the process and making a recommendation for improvement. You observe the ER and document the following information about their process.

When a patient visits the emergency room they must move through several stages. The first step is check$-$in where they must provide their personal information to the receptionist. There are three receptionists on staff at a time and the average time for them to check$-$in a patient is $7$ minutes. Next the patient will wait in the lobby until a triage nurse is available. There are $12$ triage nurses on staff during each $12$ hour shift. It takes a triage nurse an average of $20$ minutes to evaluate a patient. Then the patient will see a doctor or nurse practitioner to receive treatment. The average treatment time is $15$ minutes and there are $6$ doctors on shift at a time. Finally, the patient is ready for admission to a hospital floor or discharge. On average this process takes $30$ minutes and there are $5$ staff members assigned to complete it$.$