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Each morning during rush hour, 10,000 people want to travel from New Jersey to New York City. If a person takes the commuter train, the trip lasts 40 minutes. If x thousand people per morning drive to New York, it takes 20 + 5x minutes to make the trip. This problem illustrates a basic fact of life: If people make their decisions individu- ally, they will cause more congestion than is actu- ally necessary. a. Show that if people make their decisions indi- vidually, an average of 4000 people will travel by road from New Jersey to New York. Here you should assume that people will divide up between the trains and roads in a way that makes the aver- age travel time by road equal to the travel time by train. When this “equilibrium" occurs, nobody has an incentive to switch from the road to the train or vice versa. b. Show that the average travel time per person is minimized if 2000 people travel by road.

Each morning during rush hour, 10,000 people want to travel from New Jersey to New York City. If a person takes the commuter train, the trip lasts 40 minutes. If x thousand people per morning drive to New York, it takes 20 + 5x minutes to make the trip. This problem illustrates a basic fact of life: If people make their decisions individu- ally, they will cause more congestion than is actu- ally necessary. a. Show that if people make their decisions indi- vidually, an average of 4000 people will travel by road from New Jersey to New York. Here you should assume that people will divide up between the trains and roads in a way that makes the aver- age travel time by road equal to the travel time by train. When this “equilibrium" occurs, nobody has an incentive to switch from the road to the train or vice versa. b. Show that the average travel time per person is minimized if 2000 people travel by road.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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What's a good approach to this question using Excel?  It's on Opimization. Thank you.

70. Each morning during rush hour, 10,000 people want to travel from New Jersey to New York City. If a person takes the commuter train, the trip lasts 40 minutes. If x thousand people per morning drive to New York, it takes 20 + 5x minutes to make the trip. This problem illustrates a basic fact of life: If people make their decisions individu- ally, they will cause more congestion than is actu- ally necessary. a. Show that if people make their decisions indi- vidually, an average of 4000 people will travel by road from New Jersey to New York. Here you should assume that people will divide up between the trains and roads in a way that makes the aver- age travel time by road equal to the travel time by train. When this "equilibrium" occurs, nobody has an incentive to switch from the road to the train or vice versa. b. Show that the average travel time per person is minimized if 2000 people travel by road.
Transcribed Image Text:70. Each morning during rush hour, 10,000 people want to travel from New Jersey to New York City. If a person takes the commuter train, the trip lasts 40 minutes. If x thousand people per morning drive to New York, it takes 20 + 5x minutes to make the trip. This problem illustrates a basic fact of life: If people make their decisions individu- ally, they will cause more congestion than is actu- ally necessary. a. Show that if people make their decisions indi- vidually, an average of 4000 people will travel by road from New Jersey to New York. Here you should assume that people will divide up between the trains and roads in a way that makes the aver- age travel time by road equal to the travel time by train. When this "equilibrium" occurs, nobody has an incentive to switch from the road to the train or vice versa. b. Show that the average travel time per person is minimized if 2000 people travel by road.
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