Posted by Jake on Wednesday, March 7, 2012 at 7:47pm.
Could someone help me setup an equation for this equation?

A city bus system carries 4000 passengers a day throughout a large city. The cost to ride the bus is $1.50/person. The owner realizes that 100 fewer people would ride the bus for each $0.25 increase in fare, and 100 more people would ride for each $0.25 decrease in fare.
If the capacity of the bus system is 5000 passengers, what should the bus system charge to produce the largest possible revenue?

Calculus  MathMate, Wednesday, March 7, 2012 at 8:20pm
Let
c=cost of fare
P(c)=number of passengers at cost c
then
P(c)=4000(c1.50)*100/0.25
=4000400c+600
=4600400c
R(c)=c*P(c)
Differentiate R with respect to c, equate the derivative to zero and solve for c.
Note:
(1) c may or may not be a multiple of $0.25.
(2) The result may look ridiculous because the fixed and variable costs have not been accounted for.

Calculus  Jake, Wednesday, March 7, 2012 at 8:27pm
I keep getting the wrong answer : I don't know what I have done wrong...

Calculus  MathMate, Wednesday, March 7, 2012 at 8:50pm
What did you get, and how did you get your answer?

Calculus  Melinda, Wednesday, March 7, 2012 at 8:54pm
I used this
R(c)=(5000)(4600400c)
R'(c)=200,000
in the question it says:
The owner realizes that 100 fewer people would ride the bus for each $0.25 increase in fare, and 100 more people would ride for each $0.25 decrease in fare.
So wouldn't it be (1000.25) and (100+0.25)

Calculus  MathMate, Wednesday, March 7, 2012 at 11:24pm
It is not exactly a linear function.
P(c)=4600400c
represents the number of riders.
There is nothing in the question that requires the ridership to be 5000 to get the maximum profit.
The revenue is the product of ridership, P(c), and the ticket price, c.
So revenue is indirectly a function of the ticket price, i.e.
R(c)=cP(c)=c(4600400c)=4600c400c^2
R'(c)=4600800c=0 =>
c=5.75, an exorbitant price for a ride.
The corresponding ridership is
P(5.75)=4600400*5.75=2300
The corresponding revenue is
R(5.75)=2300*5.75=13225
Check:
R(6)=13200 < 13225
R(5.5)=13200 < 13225
So R(5.75) is indeed the maximum.

Calculus  Anonymous, Friday, February 15, 2013 at 7:30am
A pizza shop ia having
Answer This Question
Related Questions
 Deepa  A bus service carries 10 000 people daily between Ajax and Unoin Station...
 algebra 2  A drama club is planning a bus trip to new york city to see a ...
 psych  Given the following problem: Pretend that you are a bus driver. You ...
 ALGEBRA 1  A nonstop bus ride from the bus station in Atlantic City, New Jersey...
 statistics  on the daily run of an express bus, the average number of ...
 Maths  There are x people in the bus. When the bus stops y people get off and 6...
 science  The bus driver's manager wants to know the average speed at which the ...
 science  The bus driver's manager wants to know the average speed at which the ...
 science  A bus travels from city x due east toward city y. If the bus travels ...
 Math  The number of women passengers in a bus was X. The number of children in ...
More Related Questions