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 $4 per guest and averaged 80 guests per night. The next week you charged $9 per guest and averaged 45 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) = -27p +547 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 p dollars per guest, then Swing Haven breaks even. or