The Management Science Association (MSA) has arranged to hold its annual conference at the Riverside Hotel in Orlando next year. Based on historical data, the MSA believes the number of rooms it will need for its members attending the conference is normally distributed, with a mean of 800 and a standard deviation of 270. The MSA can reserve rooms now (1 year prior to the conference) for $80; however, for any rooms not reserved now, the cost will be at the hotel’s regular room rate of $120. The MSA guarantees the room rate of $80 to its members. If its members reserve fewer than the number of rooms it reserves, MSA must pay the hotel for the difference, at the $80 room rate. If MSA does not reserve enough rooms, it must pay the extra cost—that is, $40 per room.
a. Using Crystal Ball, determine whether the MSA should reserve 600, 700, 800, 900, or 1,000 rooms in advance to realize the lowest total cost.
b. Can you determine a more exact value for the number of rooms to reserve to minimize cost?