Step 1: Understanding the Concept:
To maximize revenue, we need to distribute 55 people into 25 rooms such that the total price is maximized. We compare the revenue generated per person:
Single: \(2000/1 = 2000\) per person.
Double: \(3000/2 = 1500\) per person.
Triple: \(3500/3 \approx 1167\) per person.
However, since we have a room limit (25), maximizing revenue means spreading people across as many rooms as possible at the highest room rate.
Step 2: Key Formula or Approach:
Revenue = \(2000 \times S + 3000 \times D + 3500 \times T\).
Constraints: \(S + D + T = 25\) and \(1S + 2D + 3T = 55\).
Step 3: Detailed Explanation:
Using all 25 rooms generally yields higher revenue than packing people into fewer rooms.
Let's try to maximize the higher-priced room types (Double and Triple) while using all 25 rooms.
If we use \(T\) triple rooms and \(D\) double rooms:
\(D + T = 25 \implies D = 25 - T\)
Substitute into the capacity equation:
\(2(25 - T) + 3T = 55\)
\(50 - 2T + 3T = 55 \implies T = 5\).
So, \(T = 5\) and \(D = 25 - 5 = 20\).
Revenue = \(20 \times 3000 + 5 \times 3500 = 60000 + 17500 = 77500\).
If we used single rooms, we would run out of rooms much faster (e.g., 25 singles only hold 25 people). Spreading 55 people over 25 rooms forces a mix of doubles and triples.
Step 4: Final Answer:
The maximum possible revenue is Rs. 77500.