You are the catering manager for the Imperial Palace Hotel. Last Saturday your staff catered a wedding reception in the main ballroom, during which $152$ chicken dinners, $133$ steak dinners, and $95$ fish dinners were served. All dinners are the same price. The hotel charges "per person" for catered events.

a$.$ What percent of the total meals served was each type of dinner?

b$.$ If $$13,300$ was charged for all the meals, how much revenue did each type produce?

c$.$ If a $20\%$ price increase goes into effect next month, what will be the new price per meal?

d$.$ When photographers, florists, DJs$,$ bands, and other outside vendors are booked through your office for events at the hotel, a $5\frac{1}{2}\%$ "finder's fee" is charged. Last year $$175,000$ of such services were booked. How much did the hotel make on this service?

e$.$ If your boss is expecting $$11,000$ in "finder's fee" revenue next year, what amount of these services must be booked?