. (4 points) 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 $10 per guest and averaged 300 guests per night. The next week you charged $15 per guest and averaged 250 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. b) Find the nightly revenue R(p) as a function of the cover charge p.. c) 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 $3000. Find the cost C (p) as a function of the cover charge p. (1) Now nd the prot function in terms of the cover charge p. Hence, determine the cover charge you should charge for a maximum prot