Case 3. (Show all your works: including all computational procedures and details)

(3.1) Global Airlines (GA) runs daily flights from Seoul to Hong Kong. There are two price classes (Economy class and Business class) for the seats. GA charges $400 per one-way ticket for the Economy class, and $1,400 per one-way ticket for the Business class. There are 80 seats available on a plane. Distribution of demand for Business class is known, demand for Economy class is unlimited. How many seats should the GA allocate to the Business class to maximize expected profit.

(a) Assume that cumulative demand for the Business class distribution is given as

(b) Assume now that GA is adopting a new policy. In the new policy, whenever empty Business class seats appear, the company fills the empty seats by allowing new Economy class passengers to board the airplane and up-grades their tickets to Business class (note that these consumers still pay $400). Assume that demand for the Business class distribution is a normal distribution with mean 50 and standard deviation 20.