P1: Revenue Management Doubletree in Austin has 150 standard rooms. Doubletree generally sells those rooms through two channels, one through their own website, call center and front desk usually at a high rate and the other through agencies like Priceline at a low rate. Suppose Doubletree charges a high rate at $120 per room per night through their own channel (they never mark down the price through their own explicit channel to avoid any bad gambling image which hurts reputation) while "implicitly" sells some rooms to the agencies at a low rate of S50 per room per night. Bargain customers who seek low rate usually will buy far in advance of the premium customers through the agency channel. To make it simple, suppose the customers always stay for one night, there is ample demand from the bargain customers for the low rate, and the number of uncertain which is distributed according to the following table: premium customers is however Number of high Probability fare customers S0 90 100 110 120 130 0.1 0.1 0.2 0.2 0.2 0.2 (a) How many rooms shall Doubletree sell to the agencies like Priceline in advance? (b) What is the total expected revenue (including both low and high rate customers) that Doubletree can obtain based on your solution to (a)'? (c) The number of no-shows at Doubletree has a distribution as that in the following table Doubletree estimates the cost of bumping a customer is $200. What is the optimal maximum number of reservations to accept per day (suppose overbooked rooms are only sold to the agency channel at $50)? Number of no-shows Probabilitv 0 0.05 0.05 0.1 0.1 0.2 0.2 0.2 0.1 6