Question

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 330 guests per night. The next week you charged $10 per guest and averaged 300 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 $4 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.

What formula do I use and how should I approach this problem?

Thank you.