Planning for a major redesign, Beth collected data at her store on several consecutive Saturday mornings. She noticed that customers arrived at the checkout at a rate of approximately 100 per hour. Fully 25 percent of the customers had 10 items or less. Those people took about 2 minutes to serve on average, while customers with more than 10 items took about 4 minutes to process. Beth expects service time to improve when new scanners are installed in the revised design. Help Beth with her design for the system. She would like to achieve a service level of approximately 80%-90% and an average waiting time in any line approximately between 3-7 minutes.

Hint: Note that the service level equals the system utilization coefficient ρ = λ/(Sμ). Therefore, if you assume ρ = 0.8 (or 0.9), you can determine the initial/desired S (the number of channels in an M/M/S system) after you plug in your relevant λ and μ into the formula for ρ. This is all I can help you with. I will not be answering ANY OTHER questions in this regard.

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