Ramaryatt Inn is a hotel chain with properties in numerous markets. In their New York City property, they are currently allowed to book up to 230 rooms, which is 50% of their total capacity. They offer standard rooms with two price levels: Full Rack rate at $400/night and Discount rate at $150/night. For a weekend night in May, they expect demand at the Full Rack rate has a mean of 45, a standard deviation of 16, and we assume it follows a normal distribution. (For this question, you can ignore multi-night stays.)

Discount fare customers must buy their tickets three weeks in advance, and these tickets normally sell out.

(a) How many rooms (Q) would you protect for a weekend night in May for the Full Rack-rate customers? What is the expected revenue on this flight. (Assume ample demand for Discount guests.)

(b) Suppose the forecast for Discount guests has dropped. It is now assumed that the demand for this class is normally distributed with a mean of 150 rooms and a standard deviation of 30 rooms. How many seats (Q) should Romaryatt protect for Full Rack-rate customers now?

(c)To mitigate the sudden drop in demand for Discount rooms, Romaryatt has decided to add a third room rate: a $100 per room Super Saver rate with a 6-week advanced purchase restriction. Romaryatt estimates that there is ample demand for this new rate level.

How many Super Saver rooms (S) should the Romaryatt sell? (Assume the demand for Discount rooms remains as in part (b) and for Full Rack-rate rooms as in part (a)).

Just looking help for c, was able to figure out a and b. Thanks!