Question

The University of Cincinnati Center for Business Analytics is an outreach center that collaborates with industry partners on applied research and continuing education in business analytics. One of the programs offered by the center is a quarterly Business Intelligence Symposium. Each symposium features three speakers on the real-world use of analytics. Each of the corporate members of the center (there are currently 10) receives five free tickets to each symposium that they can either use themselves or distribute to colleagues or friends. Nonmembers wishing to attend must pay $75 for a ticket per person. The ticket for each registrant (member or non-member) includes breakfast, lunch, and free parking. The following are the costs incurred on the center for putting on this event: Rental cost for the auditorium: $1000 for up to 150 attendees, but $4000 for more than 150 attendees Registration Processing: $8.50 per person Speaker Costs: 3@$500 $1,500 Continental Breakfast: $4.00 per person if catered for 120 people or less, $480 total (not per person any more) for more than 120 people Lunch: $7.00 per person if catered for 120 people or less, $6.00 per person if catered for more than 120 people Parking: $5.00 per person (a) Assume that all individuals that have a ticket in hand show up for the event. What would be the total profit of setting up this event if the center sells 50 tickets to non-members? (Round your answer to 2 decimal places) $ What would be the total profit if the center sells 127 tickets to non-members instead? (Round your answer to 2 decimal places) $ (b) If the center could sell any number of non-member registration tickets between 50 and 150 (i.e. in increments of 1), selling how many non-member tickets would maximize the center’s profit? What would be the profit if the above best number of non-member tickets were sold? $ (c) The center is considering a refund policy for no-shows. No refund would be given for members who do not attend, but for non-members who do not attend, 50% of the price will be refunded. Extend the model you developed in part (a) to account for the fact that historically, 25% of members who registered do not show and 10% of registered non-members do not attend. The center pays the caterer for breakfast and lunch based on the number of registrants (not the number of attendees). However, the center only pays for parking for those who attend. The cost of auditorium rental is also based on planned attendees (not those registered). What is the profit if each corporate member registers their full allotment of tickets and 127 nonmembers register? To help in your spreadsheet development, make sure that you first calculate the number of member attendees, the number of non-member attendees, and the total attendees. It is OK if the number of attendees becomes fractional, these numbers represent average number of people attended. If required, round your answer to two decimal places. $ (d) If the center could sell any number of non-member registration tickets between 50 and 150 (i.e. in increments of 1), selling how many non-member tickets would maximize the center’s profit based on part (c)? What would be the profit if the above best number of non-member tickets were sold? $

Answer 1

(a) Center sells 50 tickets to non-members

STATEMENT OF PROFIT

PARTICULARS	AMOUNT	WORKING
INCOME
MEMBERS	-	10*5 = 50 tickets. But these are free of cost.
NON MEMBERS	3,750	50*75
TOTAL INCOME	3,750
COST
RENTAL COST	1,000	Total attendees = 1
REGISTRATION PROCESSING	850	8.5 * 100
SPEAKER COST	1,500	3 * 500 (It is assumed that it includes all the cost of speakers including refreshments, parking, etc)
BREAKFAST	400	4 * 100
LUNCH	700	7 * 100
PARKING	500	5 * 100
TOTAL COST	4,950
PROFIT / (LOSS)	(1,200)

Center sells 127 tickets to non-members

STATEMENT OF PROFIT

PARTICULARS	AMOUNT	WORKING
INCOME
MEMBERS	-	10*5 = 50 tickets. But these are free of cost.
NON MEMBERS	9,525	127*75
TOTAL INCOME	9,525
COST
RENTAL COST	4,000	Total attendees = 177
REGISTRATION PROCESSING	1,504.5	8.5 * 177
SPEAKER COST	1,500	3 * 500
BREAKFAST	480	More than 120 people
LUNCH	1,062	6 * 177
PARKING	885	5 * 177
TOTAL COST	9,431.5
PROFIT / (LOSS)	93.5

(b)

CLASSIFICATION OF COST

COST	PER UNIT	TOTAL
VARIABLE COST
REGISTRATION PROCESSING	8.5
PARKING	5
FIXED COST
SPEAKER COST		1,500
SEMI VARIABLE COST
RENTAL COST
BREAKFAST
LUNCH
TOTAL COST

NOTES

RENTAL COST

$1000 for 150 attendees and $4000 for more than 150 attendees
variable portion = (4000 - 1000) / 150 =$20 per attendee

BREAKFAST

$4.00 per person if catered for 120 people or less, $480 total (not per person any more) for more than 120 people

variable portion =

(C)

Center sells 50 tickets to non-members

STATEMENT OF PROFIT

PARTICULARS	AMOUNT	WORKING
INCOME
MEMBERS	-	10*5 = 50 tickets. But these are free of cost.
NON MEMBERS	3,750	50*75
TOTAL INCOME	3,750
COST
RENTAL COST	1,000	Total attendees = 82.5
REGISTRATION PROCESSING	850	8.5 * 100
SPEAKER COST	1,500	3 * 500 (It is assumed that it includes all the cost of speakers including refreshments, parking, etc)
BREAKFAST	400	4 * 100
LUNCH	700	7 * 100
PARKING	412.5	5 * 82.5
REFUND AMOUNT TO NON MEMBERS	187.5	5 * 75 * 50%
TOTAL COST	3,350
PROFIT / (LOSS)	400

NOTES

TOTAL MEMBERS = 50

MEMBERS WHO DID NOT ATTEND = 50 *25 % = 12.5

MEMBERS WHO ATTENDED = 50 - 12.5 = 37.5

TOTAL NON MEMBERS = 50

NON MEMBERS WHO DID NOT ATTEND = 50 *10 % = 5

NON MEMBERS WHO ATTENDED = 50 - 5 = 45

ATTENDEES = 37.5 + 45 = 82.5

Center sells 127 tickets to non-members

STATEMENT OF PROFIT

PARTICULARS	AMOUNT	WORKING
INCOME
MEMBERS	-	10*5 = 50 tickets. But these are free of cost.
NON MEMBERS	9,525	127*75
TOTAL INCOME	9,525
COST
RENTAL COST	1,000	Total attendees = 114.3
REGISTRATION PROCESSING	1,504.5	8.5 * 177
SPEAKER COST	1,500	3 * 500
BREAKFAST	480	More than 120 people
LUNCH	1,062	6 * 177
PARKING	571.5	5 * 114.3
REFUND AMOUNT	476.25	12.7 * 75 *50%
TOTAL COST	6,594.25
PROFIT / (LOSS)	2,930.75

TOTAL MEMBERS = 50

MEMBERS WHO DID NOT ATTEND = 50 *25 % = 12.5

MEMBERS WHO ATTENDED = 50 - 12.5 = 37.5

TOTAL NON MEMBERS = 127

NON MEMBERS WHO DID NOT ATTEND = 127 *10 % = 12.7

NON MEMBERS WHO ATTENDED = 127 - 12.7 = 114.3

ATTENDEES = 37.5 + 114.3 = 151.8