Suppose that there are 3 classes of customers who purchase seats on an airplane: Class 1 pays $500 for each seat; Class 2 pays $300; and Class 3 pays $100. Suppose that the demand distributions for the classes of customers are given by pD (Efor -1,2,...,10 10 y+1 PD(v)- for y 0,1,2,3,... 2 z 1,2 1 z-5,6 Each seat is allocated to either a Class 1, a Class 2, or a Class 3 customer. Once allocated, the seat can only be sold to the class of customer it is designated for. Assume that N is the total number of seats available, and Nj is the number of seats allocated to Class j, for j 1,2,3 (a) For N- 1,2,...,20, determine the how the seats should be allocated. That is, your answer should consist of a set of 20 entries, with each entry being either 1, 2, or 3 (depending on which class of passenger receives that seat) (b) If a 21st seat is added, which class should it be given to, and what is the expected revenue generated by that seat?