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.

Question

(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.

Answer 1

this is just algebra, which you presumably know by now.

(a) q(p) = -15(p-9)+165 = -15p + 300
(b) R(p) = p*q = -15p^2 + 300p
(c) C(p) = 2q+1000 = 2(-15p+300)+1000 = 1600-30p
(d) P(p) = R(p)-C(p) = ...

Answer 2

Thanks!!