Question: (Multi-class Capacity Allocation DP; 5 points) Suppose that an airline has 4 seats. There are 3 fare classes: Class 1 with price $6, Class 2

(Multi-class Capacity Allocation DP; 5 points) Suppose that an airline has 4 seats. There are 3 fare classes: Class 1 with price $6, Class 2 with price $4, and Class 3 with price $3. The demand arrives in an increasing sequence of fares. Class 1 demand is 0 with probability 0.4, 1 with probability 0.3, and 2 with probability 0.3. Class 2 demand is 0 with probability 0.2, 1 with probability 0.4, and 2 with probability 0.4. Class 3 demand is 4 with probability 1.

(a) (4 points) Using dynamic programming, compute functions Vj (s) for j = 1, 2, 3 and s = 0, 1, 2, 3, 4 (Vj (s) is the value of having s seats for classes j and higher).

(b) (1 point) Based on these functions, compute the booking limits B j for classes j = 1, 2 and 3.

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