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 corporate member of the center $($there are currently $11)$ 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:

Rental cost for the auditorium $$150$

Registration processing $$8\mathrm{.}50$ per person

Speaker costs $3$@$$800=$ $$2,400$

Continental breakfast $$4\mathrm{.}00$ per person

Lunch $$7\mathrm{.}00$ per person

Parking $$5\mathrm{.}00$ per person

$($a$)$ Build a spreadsheet model that calculates a profit or loss for $100$ nonmember registrants. If required, round your answer to two decimal places.

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$($b$)$ Use Goal Seek to find the number of nonmember registrants that will make the event break even. Do not round your intermediate calculations. If required, round your answer to the nearest whole number.