In a busy medical clinic focused on flu patients, the impacts of a recent flu pandemic are becoming overwhelming for the hospital staff. The process of seeing a doctor is as follows. All patients must be triaged before seeing a doctor. The lineups ahead of the triage nurse are inefficient, one can see an average of 50 people waiting to be triaged. From there, patients can follow one of two paths: if they pay an additional fee to the triage nurse there is an "expedite option" in an adjacent unlabeled building. If a patient cannot afford the additional fee, they must stay in the official system. In both systems patients see doctors one-on-one.

The "additional fee" option is well staffed by doctors, an average of 5 doctors are working and 80 per cent of the time they are seeing patients. Expedite patients spend an average of 10 minutes in consultation with a doctor before leaving the clinic.

The "no additional fee" option is even more awful than triage for long waits. They have a large waiting room which can fit up to 100 patients, which on average is 90 per cent full. An average wait before seeing a doctor in the "no additional fee" option is 5 hours. In addition, patients in this option spend less time with a doctor once they are seen, an average of 6 minutes. Doctors in this option are overworked, seeing patients 90 per cent of the time they are working.

What is the average wait before being triaged?

Utilize the below formulas:

INV_q = INV - = CT - /

Q=h2S SL=Cs+CeCs