# Tricky Word Problem

• Jan 25th 2009, 05:39 AM
AlgebraicallyChallenged
Tricky Word Problem
Dear Forum I am having issues with the following word problem any help would be much appreciated

(13) A charter bus company has determined that the cost of providing x people a tour is
C(x) = 180.00 + 2.50 x.
A full tour is 60 people. The cost of a ticket is $15.00 plus$0.25 for each unsold ticket. Determine (a) the revenue function, (b) the profit function, (c) the company’s maximum profit, and (d) the number of ticket sales that yields the maximum profit.

• Jan 25th 2009, 09:25 AM
Constatine11
Quote:

Originally Posted by AlgebraicallyChallenged
Dear Forum I am having issues with the following word problem any help would be much appreciated

(13) A charter bus company has determined that the cost of providing x people a tour is

C(x) = 180.00 + 2.50 x.

A full tour is 60 people. The cost of a ticket is $15.00 plus$0.25 for each unsold ticket. Determine (a) the revenue function, (b) the profit function, (c) the company’s maximum profit, and (d) the number of ticket sales that yields the maximum profit.

a) The revenue function gives the revenue when $x$ tickets are sold:

$R(x)=[15+(60-x)\times 0.25]x$

That is the price of a single ticket is $\[15 +(60-x) \times 0.25]$ when $x$ tickets are sold.

b) The profit function is:

$
P(x)=R(x)-C(x)
$

.