A travel agency sells an exclusive tour to Caribbean. The agency reserves a certain number of spots in advance before it sells the trips to its customers. Once it starts selling the trips, the agency cannot reserve any extra spots beyond its initial commitment. The agency pays a $500 non-refundable reservation fee per spot, and sells it for $2000 to its customers. On the departure date, the agency pays the tour company an additional $850 per actual passenger, and an additional $75 penalty for every reserved spot not used. Demand for the tour among the agency’s customers is normally distributed with mean of 400 and variance of 9000.
How many spots Q should the agency reserve to maximize its expected contribution? (Hint: try modifying the usual shortage and surplus cost derivations to include the new information in the form C-=r-c- $850 and C+ = c + $75; the follow-up calculations of service level and Q are then straight-forward.)
What is the chance of selling more than 495 trips?
(a) 50 percent
(b) 16 percent
(c) 84 percent
(d) 68 percent