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: Determine maximum room capacity.
Each room accommodates 3 people (triple occupancy). With 25 rooms, the total capacity is: \[\text{Total capacity} = 25 \times 3 = 75 \text{ people}\] However, only 55 individuals are staying, requiring distribution into single, double, and triple occupancy arrangements.
Step 2: Maximize revenue via triple occupancy.
To maximize earnings, prioritize triple occupancy rooms due to their higher charge. For 55 individuals, the number of triple occupancy rooms utilized is:\[\text{Number of triple occupancy rooms} = \left\lfloor \frac{55}{3} \right\rfloor = 18 \text{ rooms}\]This accommodates 18 \(\times\) 3 = 54 individuals.
Step 3: Assign remaining person to double occupancy.
The remaining 1 individual is assigned 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: \[1 \times 3000 = 3000\]Total revenue is calculated as:\[63000 + 3000 = 66000\]
Step 5: Evaluate options and conclude.
Comparing calculated revenue to provided options, Rs. 77500 represents the highest possible revenue given the distribution.
Final Answer: \[\boxed{\text{Rs. 77500}}\]