An average of 80000 people visit Riverside Park each day in

An average of 80,000 people visit Riverside Park each day in the summer. The park charges $18.00 for admission. Consultants predict that for each $1.00 increase in the entrance price, the park would lose an average of 2,500 customers per day. (a) Express the daily revenue from ticket sales, R as a function of the number of $1.00 price increases, x. R=f(x)= (b) What ticket price maximizes the revenue from ticket sales? $ (round to nearest cent)

Solution

N= Number of visitors and $P = price $R = Revenue

N = 80,000 - (P-18)*2500

R = N*P = 80,000P -2,500P^2 + 45000P

R = 125000P -2,500P^2

dR/dP = 125000 - 5000P = 0 for max

P = $25 .0 for max revenue