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 $6 per guest and averaged 290 guests per night. The next week you charged $11 per guest and averaged 240 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 $3 per head. In addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $2,000. Find the cost C as 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.
p = $ per guest