Answered: Nightclub Management You have just…

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter4: Systems Of Linear Equations

Section4.3: Solve Mixture Applications With Systems Of Equations

Problem 4.60TI: The manufacturer of a weight training bench spends $120 to build each bench and sells them for $170....

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Nightclub Management 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 $5 per guest and averaged 225 guests per night. The next week you charged $12 per guest and averaged 120 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 (in dollars).

p = $ per guest

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