Question

1. An average of 50,000 people visit Riverside Park each day in the
summer. The park charges $21.00 for admission. Consultants predict
that for each $1.00 increase in the entrance price, the park would lose
an average of 3,500 customers per day.
(a) Express the daily revenue from ticket sales, R as a function of
the number of $1.00 price increases, x.
(b) What ticket price(rounded to nearest cent) maximizes the revenue
from ticket sales?
(c) What ticket price will lead to no revenue?

Answer 1

N= Number of visitors and $P = price $R = Revenue 
N = 50,000 - (P-15)*2500 
R = N*P = 50,000P -2,500P^2 + 15*2500P Answer (1) 
R = 87,500P -2,500P^2 
dR/dP = 87,500 - 5000P = 0 for max 
P = $17.50 for max revenue

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