a-Hotel, located in NYC, is operating with 120 rooms in a market where customers are heterogeneous in terms of the maximum willingness-to-pay levels (or valuation levels) they associate with the hotel and the booking time.

An outside market measurement firm has conducted a study wherein fifteen customers that previously experienced the hotel, corresponding to 1/12 of the market, indicate the valuations they attach to the hotel.

The data we used in this question is :

ID	Valuation Level
1	395
2	267
3	320
4	249
5	371
6	273
7	260
8	271
9	316
10	362
11	261
12	309
13	389
14	396
15	363

Today is the 1st of June, and assume that the hotel plans to allocate the arriving demand to the supply (i.e., rooms) for the 16th of July. For the sake of completeness, you can assume that no room had been booked before for this day. Given that housekeeping incurs $3 per room to the hotel, answer the questions below:

a. Determine the maximum profit the hotel achieves if it charges each customer the same price. Conduct your analysis in Excel.

b. Suppose the market measurement firm that a-Hotel has collaborated with has revealed that customers can be clustered into two groups: 1) customers with relatively higher valuations book the rooms close to the date of their arrival, and 2) customers with relatively lower valuations make bookings in advance. What would be the profit-enhancing pricing strategy relative to the pricing scheme described in part a) if the hotel incorporates two customer segments into the analysis? What would be the maximum profit that can be achieved by the hotel in the presence of two customer segments? How many rooms would the hotel reserve for customers with higher valuations yet book closer to the arrival day to maximize the total profit? Conduct your analysis in Excel.