Problem:
The lake city-based Maharaja Institute is preparing for a grand cultural event this year. To attract the local crowd for the event, the student body is running an offer on advance ticket booking by giving a 40% discount on tickets that are booked prior to one week before the event. However, the student body is also aware that there are customers who prefer booking tickets one the day of the event without availing of the discount offer. Therefore, they want to reserve a certain number of tickets for selling on the day of the event. It is estimated that the number of tickets sold on the day of the event would be normally distributed with a mean of 250 and a standard deviation of 60. The price of each ticket without any discount (i.e. if sold on the day of the event) is Rs. 500. The event is being organized in an auditorium which has 1000 seats. Assume: (i) all the tickets listed for the advance booking will be sold prior to one week before the event, and (ii) each ticket is for one seat. The objective of the student body is to maximize the expected revenue from the event.What are the underage and overage costs?