Please show work

. 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 S 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 prot P(p)in terms of the cover charge p. e) (1 point) Determine the cover charge you should charge for a maximum prot