Final answer:
The staff member follows a strategy of recommending the guestroom with the highest rate and then moving down to the next price level if rejected.
Step-by-step explanation:
The strategy followed by the staff member is to recommend the guestroom with the highest rate and then move down to the next price level if rejected. This strategy allows the staff member to start with the most expensive option and gradually find a price point that the guest finds acceptable. By offering the highest rate first, the staff member maximizes the potential revenue from the guest.