Nightclub Management You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the

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Nightclub Management You havejust opened a new nightclub, Russ' Techno Pitstop, but are unsureof how high to set the cover charge (entrance fee). One week youcharged $8 per guest and averaged 240 guests pernight. The next week you charged $10 per guest andaveraged 200 guests per night.
(a)
Find a linear demand equation showing the number ofguests q per night as a function of the covercharge p.
q(p) =
(b)
Find the nightly revenue R as a function ofthe cover charge p.
R(p) =
(c)
The club will provide two free non-alcoholic drinks for eachguest, costing the club $2 per head. In addition, the nightlyoverheads (rent, salaries, dancers, DJ, etc.) amount to $1,000.Find the cost C as a function of the covercharge p.
C(p) =
(d)
Now find the profit in terms of the covercharge p.
P(p) =
Determine the entrance fee you should charge for a maximumprofit (in dollars).
p = $ per guest