A roller coaster is being designed for a new theme park. Two "trains" are on the track at any given time. One train is being unloaded/reloaded while the other is moving along the track. The track itself takes 10 minutes to complete. The train being loaded should depart before the arriving train is no closer than one minute away. Each car of a train accommodates four people. Loading a car is estimated to take 6 seconds per passenger. Unloading is estimated to take 6 seconds per passenger. Suppose that (unlike actual roller coasters), only one car can be loaded or unloaded at a time. Unloading can NOT occur at the same time as loading. In order to maximize the number of potential passengers, how many cars should the train be made up of? Round your answer to the nearest whole car.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.5: Analytic Steady-state Queueing Models
Problem 37P
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A roller coaster is being designed for a new theme park. Two "trains" are on the track
at any given time. One train is being unloaded/reloaded while the other is moving
along the track. The track itself takes 10 minutes to complete. The train being loaded
should depart before the arriving train is no closer than one minute away.
Each car of a train accommodates four people. Loading a car is estimated to take 6
seconds per passenger. Unloading is estimated to take 6 seconds per passenger.
Suppose that (unlike actual roller coasters), only one car can be loaded or unloaded
at a time. Unloading can NOT occur at the same time as loading.
In order to maximize the number of potential passengers, how many cars should the
train be made up of? Round your answer to the nearest whole car.
Transcribed Image Text:A roller coaster is being designed for a new theme park. Two "trains" are on the track at any given time. One train is being unloaded/reloaded while the other is moving along the track. The track itself takes 10 minutes to complete. The train being loaded should depart before the arriving train is no closer than one minute away. Each car of a train accommodates four people. Loading a car is estimated to take 6 seconds per passenger. Unloading is estimated to take 6 seconds per passenger. Suppose that (unlike actual roller coasters), only one car can be loaded or unloaded at a time. Unloading can NOT occur at the same time as loading. In order to maximize the number of potential passengers, how many cars should the train be made up of? Round your answer to the nearest whole car.
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