4. You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure how high to set the cover charge (entrance fee). One week you charged \$7 per guest and averaged 180 guests per night. The next week you charged $15 per guest and averaged 100 guests per night a) (1 point) Find a linear demand equation showing the number of guests q per night as a function of the cover charge p,q(p). b) (1 point) Find the nightly revenue R(p) as a function of the cover charge p. c) (1 point) The club will provide two free nonalcoholic drinks for each guest, costing the club $3 per head. In addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $1000. Find the cost C(p) as a function of the cover charge p. d) (1 point) Find the profit P(p) in terms of the cover charge p. e) (1 point) Determine the cover charge you should charge for a maximum profit