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On a given Delhi - Mumbai trip by train, there are 200 seats. Suppose the ticket price is 475 rupies on average and the number of passengers who reserve but do not show up is normally distributed with mean 30 and standard dev 15. The company decide to overbook the trip and estimate that the average loss from passengers who will have to be bumped is 800 rupies.

(a) What is the máximum number of reservations that should be accepted? Suppose you allowed 220 reservations, how much do you expected to pay out in compensation to bumped passengers?

(b) Continue assuming 220 reservations. What is the probability that you will have to deal with bumped passengers?

Now asume that there is no overbooking and the high fare is 675 rupies and the low fare, 375 rupies. Demand for the low fare is abundant while for high fare demand is normally distributed with mean of 80 and standard dev of 35.

(d) What is the probability of selling 200 reservations if you set an optimal protection level for the full fare?

(e)Suppose a protection level of 85 is established. What  is the average number of lost high fare passengers and what is the expected number of empty seats?

(f) Continue assuming a protection level of 85. What is the expected revenue of the trip?

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