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Dr. Chan Poh Chuan, a pediatrician, is well known for his scholarly contributions to child mental well-being. To make parents aware of the issue, he holds free information sharing sessions every Friday night in his office. In the session, he discusses potential mental issues in the children and answers any questions parents may have. The meeting room where he conducts the session has a seating capacity of ten people, and because of limited capacity, reservations are required to attend the session.
But the sessions are not always full, and Dr. Chan cancels a session if two or fewer people have registered for the week’s session. Based on the data for the last year, Dr. Chan’s secretary found out the distribution of reservations as follows: “Table 2 attached” The people who attend the free session are encouraged to attend an advanced session, but the advanced session is not free of charge.
(a) Dr. Chan realized the probability of having ten reservations for a session seems incorrect. Analyze whether his calculations are correct or not.
(b) On average, how much profit can be generated for conducting the sessions?
(c) If Dr. Chan does not cancel any free sessions because of low registration, how does the profit change, on average?
(d) Some of the attendees pointed out that the registration fee for the advanced session stopped them from attending the advanced session. Dr. Chan estimated if the session fee is changed to $200 per pax, the percentage of people registering for the advanced session will increase to 50% of the people attending the free sessions. Comment whether the profit would increase under this new registration fee.
(e) Dr. Chan wants to find out what value of the registration fee can make the sessions profitable. Discuss how you should approach the problem. Determine the best value of the registration fee. Use the parameters used in the initial problem. Show your results in tabular form.
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