SOLUTION: A city centre tour guide currently charges $34 for a full day’s tour. The average number of
customers is 48. Market research suggests that for every $1 increase in tour price,
Algebra.Com
Question 1172717: A city centre tour guide currently charges $34 for a full day’s tour. The average number of
customers is 48. Market research suggests that for every $1 increase in tour price, the guide can
expect to lose two customers per tour.
(a) Show that if the price increase is $x, then the expected revenue from each tour is
−2x
2
− 20x + 1632
(b) The guide needs to ensure that the expected revenue is at least $1440. By solving a quadratic
inequality, find the range of prices that need to be charged.
(c) What price should be charged to maximize expected revenue?
Found 2 solutions by Solver92311, ankor@dixie-net.com:
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!
Why did you post the same question more than once?
John
My calculator said it, I believe it, that settles it
From
I > Ø
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A city centre tour guide currently charges $34 for a full day’s tour. The average number of customers is 48.
Market research suggests that for every $1 increase in tour price, the guide can
expect to lose two customers per tour.
(a) Show that if the price increase is $x, then the expected revenue from each tour is
:
Revenue = price * no. of customers
R(x) = (34+x)*(48-2x)
FOIL
R(x) = 1632 - 68x + 48x + -2x^2
Combine like terms. Arrange as a quadratic
R(x) = -2x^2 - 20x + 1632
:
:
(b) The guide needs to ensure that the expected revenue is at least $1440. By solving a quadratic inequality, find the range of prices that need to be charged.
:
-2x^2 - 20x + 1632 >= 1440
-2x^2 - 20x + 1632 - 1440 >= 0
-2x^2 - 20x + 192 >= 0
simplify, divide by -2
x^2 + 10x - 96 <= 0, negative mult, reverses inequality
Factors to
(x+16)(x-6) <= 0
positive solution
x <= 6 (a price increase from 34)
x >= -16 (a price drop from 34)
price range from $40 (34+6)
(34+6)(48-12) = 1440
and
to $18 (34-16)
(32-16)(48+32) = 1440
Price range $18 to $40 to make at least $1440
:
:
(c) What price should be charged to maximize expected revenue?
This will occur on the axis of symmetry where a=-2, b =-20
x =
x = -5
(34-5)(48-2(-5)) =
29 * (48+10) = $1682 is max revenue
Graphically is will make more sense. Green line is $1440
RELATED QUESTIONS
Please solve this
A city centre tour guide currently charges $34 for a full day’s... (answered by Solver92311)
Please solve this
A city centre tour guide currently charges $34 for a full day’s... (answered by Solver92311)
1.Suppose an object is thrown upward with an initial velocity of 52 feet per second from... (answered by ikleyn)
There are two different tours for a cave. The Palace tour and the lake tour. The Total... (answered by josmiceli)
Jovanna gives a walking tour of a popular tourist city to one person for $43. To... (answered by stanbon)
The number of men in a tour group is 15 times the number of women. If there are 48 people (answered by tommyt3rd)
228 people have registered for a sightseeing tour of the grand canyon. if a tour director (answered by JulietG)
You are part of the group taking a tour of the cave. tour cost six dollars for adults and (answered by macston)
Mona Kalini gives a walking tour of honolulu to one person for $47. To increase her... (answered by jenrobrody)