Answer to Question #8178 in Algebra for Beverly Beauchamp

Question

Maximizing Revenue The regular price for a
round-trip ticket to Las Vegas, Nevada, charged by an
airline charter company is $300. For a group rate the
company will reduce the price of each ticket by $1.50
for every passenger on the flight.
(a) Write a formula f(x) that gives the revenue from
selling x tickets.
(b) Determine how many tickets should be sold to maximize
the revenue. What is the maximum revenue?

Answer 1

(a) The revenue of selling x tickets is given by formula: f(x)=( 300 - 1.50x
)x
(b)f"(x)= 300 - 3x . Maximum revenue will be if f'(x)=0 :

300-3x=0
x=100
The maximum revenue is $15000 if should be sold 100
tickets.