1. Pegasus Airlines is planning their flights between different cities of Turkey. We focus on the flight they will have on March 7th of this year, that departs from İzmir, stops in İstanbul and continues to Kayseri. The plan is to sell the tickets to three types of passengers: the ones traveling from İzmir to İstanbul (passenger type 1), the ones traveling from İstanbul to Kayseri (passenger type 2), and the passengers traveling from İzmir to Kayseri (passenger type 3). The airplane can seat 30 passengers, and the airline offers three fair classes of economy (E), business (B) and first class (F). Ticket prices have been set and advertised as Pij, where i refers to the passenger type and j represents the fair classes. Also, based on past experiences demand forecasters have determined the upper bounds on the number of potential customers of tij for all origin-destination/ fair class combinations. The aim is to find the number of tickets to sell to each of these 9 combinations with the maximum revenue. (a) Formulate this as an integer programming problem without overbooking or exceeding the forecasted maximum demand. (b) Consider the case where the airline needs to pay taxes for each flight route as follows: If the sold tickets are less than 16 then they would pay $1000 per passenger, else $2400 per passenger. How would you incorporate this requirement into your model?