The most popular cruise offered by Luxury Cruises is a three-week cruise in the Mediterranean each July with daily ports of call at interesting tourist destinations. The ship has 1,000 cabins, so it is a challenge to fill the ship because of the high fares charged. In particular, the average regular fare for a cabin is $20,000, which is too high for many potential customers. Therefore, to help fill the ship, the company offers a special discount fare for this cruise that averages $12,000 per cabin when it announces its future cruises a year in advance. The deadline for obtaining this discount fare is 11 months before the cruise, and this discount also can be discontinued earlier at the company’s discretion. Thereafter, the company uses heavy publicity to attract luxuryseeking customers who make vacation plans later and are willing to pay the regular fare averaging $20,000 per cabin. Based on past experience, it is estimated that the number of such luxury-seeking customers for this cruise has a normal distribution with a mean of 400 and a standard deviation of 100.
Use the model for capacity-controlled discount fares presented in Sec. 18.8 to determine the maximum number of cabins that should be sold at the discount fare before reserving the remaining cabins to be sold at the regular fare.