Discuss the following in detail:
The Delacroix Inn in Alexandria is a small exclusive hotel with 20 rooms. Guests can call housekeeping from 8:00 am to midnight for any of their service needs. Housekeeping keeps one person on duty during this time to respond to guest calls. Each room averages 0.7 call per day to housekeeping (Poisson Distributed), and a guest requires an average response time of 30 minutes (exponentially distributed) from the staff person. Determine the portion of time the staff person is busy and how long a guest must wait for his or her request to be addressed. Does the housekeeping system seem adequate?