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A proposal has been presented to the government of Newfoundland and Labrador that would build a new section of highway which would provide improved access for residents of a remote coastal area near Bonavista. The highway would be 16 kilometres in length. The initial proposal called for 7 toll booths, each staffed by an employee. But a subsequent proposal recommended replacing the employees with machines. Many factors must be considered because the intended employees are unionized. However, one of the government's concerns is the effect that replacing the employees with machines will have on the times the drivers spend in the system. Customers will arrive to any one toll booth at a rate of 9 per minute. In the exact-change lanes with employees, the service time is essentially constant at 5 seconds for each driver. With machines, the average service time would still be 5 seconds, but it would be exponential rather than constant, because it takes time for the coins to rattle around in the machine. Contrast the two systems for a single lane. tak

A proposal has been presented to the government of Newfoundland and Labrador that would build a new section of highway which would provide improved access for residents of a remote coastal area near Bonavista. The highway would be 16 kilometres in length. The initial proposal called for 7 toll booths, each staffed by an employee. But a subsequent proposal recommended replacing the employees with machines. Many factors must be considered because the intended employees are unionized. However, one of the government's concerns is the effect that replacing the employees with machines will have on the times the drivers spend in the system. Customers will arrive to any one toll booth at a rate of 9 per minute. In the exact-change lanes with employees, the service time is essentially constant at 5 seconds for each driver. With machines, the average service time would still be 5 seconds, but it would be exponential rather than constant, because it takes time for the coins to rattle around in the machine. Contrast the two systems for a single lane. tak

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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A proposal has been presented to the government of Newfoundland and Labrador that would build a new section of highway which would provide improved access for residents of a remote coastal area near Bonavista. The highway would be 16 kilometres in length. The initial proposal called for 7 toll booths, each staffed by an employee. But a subsequent proposal recommended replacing the employees with machines. Many factors must be considered because the intended employees are unionized. However, one of the government's concerns is the effect that replacing the employees with machines will have on the times the drivers spend in the system. Customers will arrive to any one toll booth at a rate of 9 per minute. In the exact-change lanes with employees, the service time is essentially constant at 5 seconds for each driver. With machines, the average service time would still be 5 seconds, but it would be exponential rather than constant, because it takes time for the coins to rattle around in the machine. Contrast the two systems for a single lane. h For the "Exact Change Lane" with employee (round your responses to two decimal places): The average time driver spends waiting to pay the toll is seconds. The average time spent by a driver in the toll system (waiting and paying) is seconds. The average number of drivers waiting in the line to pay the toll at a toll booth is drivers. The average number of drivers at any toll booth, namely, in the system is drivers.
Transcribed Image Text:A proposal has been presented to the government of Newfoundland and Labrador that would build a new section of highway which would provide improved access for residents of a remote coastal area near Bonavista. The highway would be 16 kilometres in length. The initial proposal called for 7 toll booths, each staffed by an employee. But a subsequent proposal recommended replacing the employees with machines. Many factors must be considered because the intended employees are unionized. However, one of the government's concerns is the effect that replacing the employees with machines will have on the times the drivers spend in the system. Customers will arrive to any one toll booth at a rate of 9 per minute. In the exact-change lanes with employees, the service time is essentially constant at 5 seconds for each driver. With machines, the average service time would still be 5 seconds, but it would be exponential rather than constant, because it takes time for the coins to rattle around in the machine. Contrast the two systems for a single lane. h For the "Exact Change Lane" with employee (round your responses to two decimal places): The average time driver spends waiting to pay the toll is seconds. The average time spent by a driver in the toll system (waiting and paying) is seconds. The average number of drivers waiting in the line to pay the toll at a toll booth is drivers. The average number of drivers at any toll booth, namely, in the system is drivers.
For the lane with the proposed machine (round your responses to two decimal places): The average time driver spends waiting to pay the toll is seconds. The average time spent by a driver in the toll system (waiting and paying) is The average number of drivers waiting in the line to pay the toll at a toll booth is The average number of drivers at any toll booth, namely, in the system is drivers. seconds. drivers. As a result of proposed change, the average time spent per driver waiting in the line to pay the toll increases by % (round your response to the nearest whole number). As a result of proposed change, the average time spent per driver in the toll system increases by % (round your response to the nearest whole number). As a result of proposed change, the average number of drivers waiting in the line to pay the toll increases by % (round your response to the nearest whole number). As a result of proposed change, the average number of drivers at any toll booth increases by % (round your response to the nearest whole number).
Transcribed Image Text:For the lane with the proposed machine (round your responses to two decimal places): The average time driver spends waiting to pay the toll is seconds. The average time spent by a driver in the toll system (waiting and paying) is The average number of drivers waiting in the line to pay the toll at a toll booth is The average number of drivers at any toll booth, namely, in the system is drivers. seconds. drivers. As a result of proposed change, the average time spent per driver waiting in the line to pay the toll increases by % (round your response to the nearest whole number). As a result of proposed change, the average time spent per driver in the toll system increases by % (round your response to the nearest whole number). As a result of proposed change, the average number of drivers waiting in the line to pay the toll increases by % (round your response to the nearest whole number). As a result of proposed change, the average number of drivers at any toll booth increases by % (round your response to the nearest whole number).
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