7. -1.25 points WaneAC5 2.1.035. My Notes You have just opened a new nightclub,

Question

7. -1.25 points WaneAC5 2.1.035. My Notes 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 $6 per guest and averaged 360 guests per night. The next week you charged $15 per guest and averaged 225 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 $4 per head. In addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $2,000. Find the cost C as a function of the cover charge p ap) = (d) Now find the profit in terms of the cover charge p. Pp) Determine the entrance fee you should charge for a maximum profit. p=$ per guest Need Help? Talk to a Tutor

Explanation / Answer

(6 , 360)
and
(15 , 225)

Slope = (225 - 360) / (15 - 6)
m = -135/9
m = -15

So, we have
q = -15p + C

using (6,360) :
360 = -15(6) + C
C = 450

So,
q = -15p + 450 ----> ANS

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b)
Reenue = p*q

R = p(-15p + 450)

R = -15p^2 + 450p --> ANS

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c)
Cost = 4*q + 2000
C = 4(-15p + 450) + 2000

C = -60p + 3800 ---> ANS

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d)
For profit, we do R - C

P = R - C

P = -15p^2 + 450p - (-60p + 3800)

P = -15p^2 + 510p - 3800

Now, for max profit,
dP/dp = 0 --> -30p + 510 = 0
p = 17

So, 17$ per guest ---> ANS

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