Nightclub ManagementYou 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 $7per guest and averaged280guests per night. The next week you charged $12per guest and averaged230guests per night.

(a)

Find a linear demand equation showing the number of guestsqper night as a function of the cover chargep.

q(p) =

(b)

Find the nightly revenueRas a function of the cover chargep.

R(p) =

(c)

The club will provide two free non-alcoholic drinks for each guest, costing the club $3per head. In addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $1,000. Find the costCas a function of the cover chargep.

C(p) =

(d)

Now find the profit in terms of the cover chargep.

P(p) =

Determine the entrance fee you should charge for a maximum profit (in dollars).

p= $per guest