There are 25 rooms in a hotel. Each room can accommodate at the most three people. For each room, the single occupancy charge is Rs. 2000 per day, the double occupancy charge is Rs. 3000 per day, and the triple occupancy charge is Rs. 3500 per day.
If there are 55 people staying in the hotel today, what is the maximum possible revenue from room occupancy charges today?

So, there are 25 rooms in total and 55 people need to be occupied in the these 25 rooms. We need to maximize the revenue.

The cost of a single, double and triple occupancy room is Rs. 2,000, Rs. 3,000 and Rs. 3,500 respectively. 

Now, if we look at the per person cost from a single, double and triple occupancy room, it will be Rs. 2,000, Rs. 1,500 and Rs. 1,166.67

Now, we clearly see that the per person cost is maximum for single occupancy room but we know that there are only 25 rooms which are not sufficient. Hence, we will aim to adjust all the 55 people to the maximum possible single occupancy then double occupancy and then triple occupancy room.

Let the number of single, double and triple occupancy rooms used are $$x$$, $$y$$ and $$z$$ respectively. 

We know $$x+y+z=25$$ as the total number of rooms are 25. 

Further, $$x+2y+3z=55$$ I.e. total number of people.

If z = 1, y = 28 which is not possible as the number of rooms are limited to 25. 

If z = 2, y = 26 which is again not possible. 

If z = 3, y = 24 which is again not possible. 

If z = 4, y = 22 which is again not possible. 

If z = 5, y = 20 which is possible. 

Hence, to maximize the revenue, we have to use 20 room of double occupancy and 5 rooms of triple occupancy. 

Hence, the total revenue will be $$20\times3,000\ +5\times3.500=77,500$$