You have just opened a new dance club, Swing Haven, but are unsure of how high to set the cover charge (entrance fee). One week you charged $5 per guest and averaged 77 guests per night. The next week you charged $12 per guest and averaged 42 guests per night. (a) Find a linear demand equation showing the number of guests q per night as a function of the cover charge p.
q(p) =

(b) Find the nightly revenue R as a function of the cover charge p.
R(p) =

(c) When you set the admission to p dollars, the club's nightly costs, including rent, salaries, and two free non-alcoholic drinks for each guest, amounts to
C(p) =−25.5p +683
Find the profit in terms of the cover charge p.
P(p) =

(d) Determine entrance fees that allow Swing Haven to break even. Enter the lower fee first, and round your answer to two decimal places.
When the entrance fee is or
dollars per guest, then Swing Haven breaks even.