1.Cooper is the manager of Hotel California. He sets the room price at $250 for weekdays, and $750 for weekend. The hotel has 350 rooms, and two classes of customers. Class-1 customers arrive during weekdays, while class-2 customers come during weekend. The demand D₁ for class-1 is uniformly distributed between 500 and 600, D₁ U[550,650]; the demand D₂ for class-2 is normally distributed, D₂ N( = 165,² = 55²).

(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 = 9. However, rejecting a customer with reservation costs the hotel $900 for accommodation and the reputation loss. What is the optimal number of reservations should Cooper book?

(d)If Cooper sets protection level to 100 rooms and overbooks customers by 15 rooms, what is the booking limit for class-1 customers?