# Calculus

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**Sydney**
.

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 $9 per guest and averaged 165 guests per night. The next week you charged $10 per guest and averaged 150 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 $2 per head. In addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $1,000. 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.