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A new takeout restaurant in a theme park is in the design process and must decide on how many walk-up windows to request in order to minimize the sum of server costs and customer waiting costs. The designer estimates each customer in the system costs $90 per hour and a server plus their station costs $30 per hour. No more than 6 walk-up windows will fit into the new building. a. How many walk-up windows should be requested if customers arrive at the rate of 64 per hour and each server at a walk-up window can handle 20 customers per hour? (Arrival and service rates follow Poisson and exponential distributions respectively) b. A vendor shows the designer new point of sale equipment that would speed up the service rate to 32 customers per hour but would add a cost of $20 per hour to each walk-up window (making the server plus walk-up window cost $50). Should the new equipment be implemented and how many walk-up windows should be used?

A new takeout restaurant in a theme park is in the design process and must decide on how many walk-up windows to request in order to minimize the sum of server costs and customer waiting costs. The designer estimates each customer in the system costs $90 per hour and a server plus their station costs $30 per hour. No more than 6 walk-up windows will fit into the new building. a. How many walk-up windows should be requested if customers arrive at the rate of 64 per hour and each server at a walk-up window can handle 20 customers per hour? (Arrival and service rates follow Poisson and exponential distributions respectively) b. A vendor shows the designer new point of sale equipment that would speed up the service rate to 32 customers per hour but would add a cost of $20 per hour to each walk-up window (making the server plus walk-up window cost $50). Should the new equipment be implemented and how many walk-up windows should be used?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A new takeout restaurant in a theme park is in the design process and must decide on how many walk-up windows to request in order to minimize the sum of server costs and customer waiting costs. The designer estimates each customer in the system costs $90 per hour and a server plus their station costs $30 per hour. No more than 6 walk-up windows will fit into the new building. a. How many walk-up windows should be requested if customers arrive at the rate of 64 per hour and each server at a walk-up window can handle 20 customers per hour? (Arrival and service rates follow Poisson and exponential distributions respectively) b. A vendor shows the designer new point of sale equipment that would speed up the service rate to 32 customers per hour but would add a cost of $20 per hour to each walk-up window (making the server plus walk-up window cost $50). Should the new equipment be implemented and how many walk-up windows should be used?
Transcribed Image Text:A new takeout restaurant in a theme park is in the design process and must decide on how many walk-up windows to request in order to minimize the sum of server costs and customer waiting costs. The designer estimates each customer in the system costs $90 per hour and a server plus their station costs $30 per hour. No more than 6 walk-up windows will fit into the new building. a. How many walk-up windows should be requested if customers arrive at the rate of 64 per hour and each server at a walk-up window can handle 20 customers per hour? (Arrival and service rates follow Poisson and exponential distributions respectively) b. A vendor shows the designer new point of sale equipment that would speed up the service rate to 32 customers per hour but would add a cost of $20 per hour to each walk-up window (making the server plus walk-up window cost $50). Should the new equipment be implemented and how many walk-up windows should be used?
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