A train service carries 20,000 people daily between Rationalia and Real City. The rail line could serve up to 60,000 people. The cost to ride the train is $pi, but research shows that for each fare increase of $0.02, ridership will go down by 271 people. a. Create a function to represent the revenue of the train service after increases of $0.02. b. Given the constraints of the problem, what is the domain of your function? c. What fare should be charged to maximize revenue? d. If each rider costs the rail service $0.10, what fare should be charged to maximize profit?
A train service carries 20,000 people daily between Rationalia and Real City. The rail line could serve up to 60,000 people. The cost to ride the train is $pi, but research shows that for each fare increase of $0.02, ridership will go down by 271 people. a. Create a function to represent the revenue of the train service after increases of $0.02. b. Given the constraints of the problem, what is the domain of your function? c. What fare should be charged to maximize revenue? d. If each rider costs the rail service $0.10, what fare should be charged to maximize profit?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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. A train service carries 20,000 people daily between Rationalia and Real City. The
rail line could serve up to 60,000 people. The cost to ride the train is $pi, but
research shows that for each fare increase of $0.02, ridership will go down by
271 people.
a. Create a function to represent the revenue of the train service after
increases of $0.02.
b. Given the constraints of the problem, what is the domain of your function?
c. What fare should be charged to maximize revenue?
d. If each rider costs the rail service $0.10, what fare should be charged to
maximize profit?
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VIEWStep 2: a) Creating function represent the revenue of the train service after increases of $0.02.
VIEWStep 3: b. Finding domain of the function:
VIEWStep 4: c. Finding fare that should be charged to maximize revenue
VIEWStep 5: Finding the fare to maximize the profit.
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