$(2-1)$suppose $80$ rooms are protected for full$-$price rooms.what is the booking limit for the discount rooms?

$(2-2)$ What is the hotel's overage cost and underage cost when determining the optimal protection level for next season?

$(2-3)$ What is the hotel's critical ratio when determining the optimal protection level for next season?

$(2-4)$ Find the optimal protection level for full$-$price rooms that maximizes the hotel's expected revenue.

$(2-5)$ If the hotel did not choose to protect any rooms for the full$-$price customers, then what would the hotel's expected revenue be$?$