Cooper is the manager of Hotel California. He sets the room price at $255 for weekdays and $750 for weekends. The hotel has 355 rooms and two classes of customers. Class-1 customers arrive during weekdays, while class-2 customers come during the weekend. The demand D1 for class-1 is uniformly distributed between 500 and 600, D1 ∼ U[500, 600]; the demand D2 for class-2 is normally distributed, D2 ∼ N (µ = 160, σ 2 = 502 ).

(a) If Cooper protects 100 rooms for class-2 customers, what is the expected revenue from class-2 customers?

(b) If Cooper wants to maximize the expected revenue, what is the optimal protection level?

(c) Cooper finds the number X of no-shows follows Poisson distribution, with mean λ = 7. However, rejecting a customer with a reservation costs the hotel $900 for accommodation and reputation loss. What is the optimal number of reservations should Cooper book? 

(d) If Cooper sets the protection level to 90 rooms and overbooks customers by 12 rooms, what is the booking limit for class-1 customers?