Three doctors, Dr. Ben, Dr. Kane and Dr. Wayne visit a particular clinic Monday to Saturday to see patients. Dr. Ben sees each patient for 10 minutes and charges Rs. 100/-. Dr. Kane sees each patient for 15 minutes and charges Rs. 200/-, while Dr. Wayne sees each patient for 25 minutes and charges Rs. 300/-.
The clinic has three rooms numbered 1, 2 and 3 which are assigned to the three doctors as per the following table.
| Room No. | Monday & Tuesday | Wednesday & Thursday | Friday & Saturday |
|---|---|---|---|
| Ben | Wayne | Kane | |
| Kane | Ben | Wayne | |
| Wayne | Kane | Ben |
The clinic is open from 9 a.m. to 11.30 a.m. every Monday to Saturday.
On arrival each patient is handed a numbered token indicating their position in the queue, starting with token number 1 every day. As soon as any doctor becomes free, the next patient in the queue enters that emptied room for consultation. If at any time, more than one room is free then the waiting patient enters the room with the smallest number. For example, if the next two patients in the queue have token numbers 7 and 8 and if rooms numbered 1 and 3 are free, then patient with token number 7 enters room number 1 and patient with token number 8 enters room number 3.
What is the maximum number of patients that the clinic can cater to on any single day?
Correct Answer :
31
Solution :
The clinic is open from 9 a.m. to 11:30 a.m., which is a total duration of 2 hours and 30 minutes, or 150 minutes.
To find the maximum number of patients the clinic can cater to on any single day, we assume the configuration of doctors in rooms 1, 2, and 3 maximizes patient throughput. The doctors have the following session lengths per patient:
- Dr. Ben: 10 minutes
- Dr. Kane: 15 minutes
- Dr. Wayne: 25 minutes
Since no specific room-to-doctor assignment table is given in the text, we calculate the absolute maximum throughput possible if all three doctors are working simultaneously for the full 150 minutes.
Number of patients seen by each doctor:
- Dr. Ben: patients.
- Dr. Kane: patients.
- Dr. Wayne: patients.
Total maximum patients = patients.
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