4. Statler Hotel is considering upgrading some of its rooms and then charging alumni extra if they want to upgrade from the Standard room to the VIP room. The cost to Statler to make the upgrade improvements is $20 per room. The opportunity cost of leaving rooms exactly as they are is zero since these costs are sunk. There are two types of Cornell alums - Frugal and Pampered. Each type of alum would like to rent one room. There are equal number of Pampered and Frugal alums. If the price is too high alums will simply stay at another nearby hotel. The following table presents the value that each type of alum (Pampered or Frugal) obtain from each type of room (VIP or Standard). VIP Pam (3er $200 $140 Fruaf $120 $100 a) What price should Statler charge for the di'erent rooms to maximize prots? (5) b) If the fraction of Pampered alums increased above 50%, at what fraction of Pampered alums would it be prot maximizing for Statler to only oiTer VIP rooms