An airline has two fare classes and protects 40 seats for the higher fare class. Assume that total capacity is 100 seats. The demand for the higher fare class ranges from 30 to 70 and it is uniformly distributed.

a) If the discount ticket costs $300, how much should the full fare ticket cost to make the protection level of 40 optimal? Hint: Use the formula p_d/p_f = P(d_f > y) = 1 - (y - a)/(b - a) for the uniformly distributed demand over [a, b].

b) Despite protecting 40 seats for the higher fare class, suppose that the airline has 45 seats remaining after selling to lower fare class. Assume that the higher fare is $350, what is the expected revenue that the airline makes from the higher fare class? To solve this problem, first draw revenue as a function of the high fare class demand. For 30 d_f 45, the revenue is 350d_f . For 45 d_f 70, the revenue is 350(45). The expected revenue is the average revenue as d_f ranges from 30 to 70. If it is easier for you, you can assume that the demand is discrete uniform and takes only integer values, so the range is {30, 31, 32, . . . , 69, 70}.