Consider again the scenario described in Problem $4.$

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. Extend the model you developed in

Problem $4$ for the Business Intelligence Symposium to account for the fact that, historically, $25\%$ 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 if each corporate member

registers their full allotment of tickets and $127$ 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 $2\%.$ At what point profit is negative?

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? What is the lowest profit?