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 |
| 1 |
Ben |
Wayne |
Kane |
| 2 |
Kane |
Ben |
Wayne |
| 3 |
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?
- $30$
- $12$
- $31$
- $15$