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.