Nightclub Management You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). One week you charged $8 per guest and averaged 240 guests per night. The next week you charged $10 per guest and averaged 200 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) The club will provide two free non-alcoholic drinks for each guest, costing the club $2 per head. In addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $1,000. Find the cost Cas a function of the cover charge p. C(p) = (d) Now find the profit in terms of the cover charge p. P(p) = Determine the entrance fee you should charge for a maximum profit (in dollars). p = $ per guest