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 $($c$)$ Consider three scenarios.

All other inputs are the same as in part $($a$).$ Use Scenario Manager to generate a summary report that gives the profit for each of these three scenarios.

What is the highest profit $($in dollars$)?$

$

What is the lowest profit $($in dollars$)?$

$

programs offered by the center is a quarterly Business Intelligence Symposium. Each symposium features three speakers on the real$-$world use of analytics. Each corporate member of the center

$($there are currently $10)$ receives five free seats to each symposium. Nonmembers wishing to attend must pay $$70$ per person. Each attendee receives breakfast, lunch, and free parking. The following

are the costs incurred for putting on this event.

$($a$)$ The Center for Business Analytics is considering a refund policy for no$-$shows. No refund would be given for members who do not attend, but nonmembers who do not attend will be refunded

$50\%$ of the price. Construct a model for the profit or loss based on the number of nonmember registrants that also accounts for the fact that, historically, $20\%$ of members who registered do not

show and $10\%$ of registered nonmembers 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 pays for parking only for those who attend. What is the profit $($in dollars$)$ if each corporate member registers their full allotment of tickets and $138$ nonmembers register?

$

$($b$)$ Use a two$-$way data table to show how profit changes as a function of number of registered nonmembers and the no$-$show percentage of nonmembers. Vary the number of nonmember

registrants from $80$ to $160$ in increments of $5$ and the percentage of nonmember no$-$shows from $10\%$ to $30\%$ in increments of $5\%.$ In which interval of nonmember registrants does breakeven

occur if the percentage of nonmember no$-$shows is $15\%?$

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