You have just opened a club, but are unsure of how high to set the cover charge
ID: 3214227 • Letter: Y
Question
You have just opened a club, but are unsure of how high to set the cover charge fee. One week you charged $10/guest and averaged 300 guests/night. The next week you charged $15 and averaged 250 guests/night. a)Find a linear demand equation showing the number of guests q/night as a funciton of the cover charge p. b)find the nightly revenue as a function of the cover charge p. c)The club will provide 2 free drinks for each guest, costing the club $3/head. The nightly overheads amount to $3000. Find the cost C as a function of the cover charge c. d) Find the profit in terms of the cover charge p and determine the cover charge you should charge for a maximum profitExplanation / Answer
Find a linear demand equation showing the number of guests q per night as a function of the cover
charge p. Answer: q = 10p + 400
b) Find the nightly revenue R as a function of the cover charge p. Answer: R = 10p
2 + 400p
c) The club will provide two free nonalcoholic drinks for each guest, costing the club $3 per head. In
addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $3000. Find the cost C
as a function of the cover charge p. Answer: C = 30p + 4200
d) Now nd the prot in terms of the cover charge p, and hence determine the cover charge you should
charge for a maximum prot. Answer: P = 10p
2 + 430p 4200; p = 21:50
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