WSpectacles is a firm that organizes concerts, festivals and spectacles in Paris. In particular, WSpectacles focuses on events for young people, e.g. rock concerts or heavy-metal festivals. The firm has an agreement with The Concert-Hall, a venue for spectacles that is available for WSpecatcles every Saturday. The Concert-Hall has a capacity for 1,000 attendance and does not have seats, so people have to stand during the spectacles. Such characteristic fits well to the requirements of WSpectacles, because most of the attendance prefers to stand during the shows. Mr. Keulls, the CEO of WSpectacles, implemented two actions in order to maximize the revenues of the firm. First, WSpectacles sells tickets by using only a single channel: the website of the firm. Tickets are posted on the website three months before the show is held (assume 90 days). For security reasons, tickets are not available the day of the concert. Second, there are two tickets category: Magic ticket: Unit price of 55 euros. With this ticket, the client accesses to The Concert Hall through priority queues (expected waiting time 7 minutes). W ticket: Unit price of 35 euros. With this ticket, the client accesses to The Concert-Hall through regular queues (expected waiting time 26 minutes). WSpectacles implemented the Magic and W tickets under the basis of a first-comefirst-served, i.e., tickets are sold according to the arrival time of the clients to the webpage. After implementing those policies, Mr. Keulls is quite dissapointed on the result of his Demand Management. Indeed, he is wondering if having two tickets categories is a good strategy. In order to improve the situation of the firm, Mr. Keulls hired an external consultant to analyze the customer behavior. This external consultant concluded the following about the demand at the beginning of the booking period: The demand for Magic tickets can be assumed uniformly (discrete) distributed, where the extreme values of the distribution are 50 and 350.

Mr. Keulls proposes a third type of category: the VIP ticket, whose price is 80 Euros. Mr. Keulls expects that this new ticket category will take a quarter of the customers of the Magic tickets. How can WSpectacles maximize the expected revenues under these new conditions?