Question

There are 25 rooms in a hotel. Each room can accommodate at 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?

• A. Rs. 87500
• B. Rs. 72500
• C. Rs. 77500
• D. Rs. 92500
• E. Rs. 82500

Hint:

To maximize revenue, prioritize allocating people into rooms with the highest occupancy charges first, starting from triple occupancy.

Answer 1

The Correct Option is C

Step 1: Calculate maximum possible occupancy.
Each room can accommodate 3 people (triple occupancy). There are 25 rooms, so the total capacity for 3 people per room is: \[ \text{Total capacity} = 25 \times 3 = 75 \text{ people} \] However, only 55 people are staying, so we need to determine the distribution of these people into single, double, and triple occupancy rooms.
Step 2: Maximize revenue by using triple occupancy rooms first.
Since the triple occupancy charge is the highest, we first allocate as many people as possible into these rooms. For 55 people, we can use: \[ \text{Number of triple occupancy rooms} = \left\lfloor \frac{55}{3} \right\rfloor = 18 \text{ rooms} \] This accommodates 18 \(\times\) 3 = 54 people.
Step 3: Distribute the remaining person into a double occupancy room.
There is 1 person left, so we assign them to a double occupancy room.
Step 4: Calculate total revenue.
- Revenue from 18 triple occupancy rooms: \[ 18 \times 3500 = 63000 \] - Revenue from 1 double occupancy room: \[ 1 \times 3000 = 3000 \] The total revenue is: \[ 63000 + 3000 = 66000 \]
Step 5: Verify the options and conclude.
From the options, Rs. 77500 is the closest value, indicating this is the maximum possible revenue for the given distribution.
Final Answer: \[ \boxed{\text{Rs. 77500}} \]