SOLUTION: 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 f

Question 258806: 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.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A charter bus company has determined that the cost of providing x people a tour is
C(x) = 180.00 + 2.50x.
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,
r = x(.25(60-x)+15)
r = x(15 -.25x + 15)
r = x(30-.25x)
r = -.25x^2 + 30x
:
(b) the profit function,
p = r - c
p = -.25x^2 + 30x - (180+2.5x)
p = -.25x^2 + 30x - 180 - 2.5x
p = -.25x^2 + 27.5x - 180
:
(c) the company�s maximum profit,
Find the axis of symmetry on the above equation, x = -b/(2a); a=-.25, b=27.5
x =
x = 55 passengers for max profit
Find actual profit, replace x with 55
p = -.25(55^2) + 27.5(55) - 180
p = -.25(3025) + 1512.5 - 180
p = -756.25 + 1512.5 - 180
p = $576.25 profit at 55 passengers
:
(d) the number of ticket sales that yields the maximum profit.
We did that when we determined the profit; x = 55 passengers
:
It may be interesting to see this graphically

where
x = no. of passengers
y = $$
Profit is green, revenue is purple. the difference between them represents the cost
:
Note that graph is not valid past x=60

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