Problem 2

The UN Association in Poverty Service (UNAPS) is going to reserve a number of tickets for a concert held in Sydney Opera House in December 2019. Based on a survey on its members, UNAPS believes the number of tickets requested is normally distributed with a mean of 500 and a standard deviation of 100. The UNAPS can reserve tickets now (six months prior to the concert) for $120 each; however, for any tickets quested beyond the reserved now, the cost will be at the regular price of $200. The UNAPS guarantees the ticket price of $120 to its members. If its members request fewer than the number of tickets it reserves, the UNAPS must pay the concert organiser for the difference with a discount, at $80 for each remaining ticket reserved one week before the concert.

Tasks:

1) Determine whether the UNAPS should reserve 400, 450, 500, 550, 600 or 650 tickets in advance to realize the lowest total cost using Crystal Ball.

2) Can you determine a more exact number or a small range of the number of tickets to reserve to minimize the cost?