A sandwich shop has three types of customers (sandwich-only, soup-only, and combo). The shop has three workstations, each staffed by a single worker (sandwich, soup, and checkout). 8 sandwich-only customers arrive each hour and spend 6 minutes at the sandwich workstation and 2 minutes at the checkout but do not visit the soup station. 5 soup-only customers arrive each hour spend 7 minutes at the soup station and 2 minutes at the checkout but do not visit the sandwich station. 4 combo customers arrive each hour and spend 5 minutes at the sandwich station, 6 minutes at the soup station and 3 minutes at the checkout. Instruction: Round your answer to the nearest 0.1 customer. What is the flow rate of sandwich-only type customers?

7.1 customers /hr.

Explanation:

The flow rate of sandwich-only type customers can be calculated by first determining the workload on each sandwich workstation

The workload on the sandwich workstation

workload = (8 sandwich-only customers per hr x 6 minutes per customer) + (4 combo customers per hr * 5 minutes per customer )

workload = (8x6) + (4x5)

workload = 68 minutes / hour

The capacity per hour for a single worker in this station = 60 minutes. So,

implied utilization = Workload / Capacity

implied utilization = (68/60)

implied utilization = 113.3%

The workload on the soup workstation

workload = (5 soup-only customers per hr x 7 minutes per customer) + (4 combo customers per hr x 6 minutes per customer )

workload = 5x7 + 4x6

workload = 59 minutes/hour

The capacity per hour for a single worker in this station = 60 minutes. So, the implied utilization is less than 100%.

The workload on the checkout workstation

workload = (8 sandwich-only customers per hr x 2 minutes per customer) + (5 soup-only customers per hr x 2 minutes per customer) + (4 combo customers per hr x 3 minutes per customer )

workload = 8x2 + 5x2 + 4x3

workload = 38 minutes/hour

The capacity per hour for a single worker in this station = 60 minutes. So, the implied utilization is less than 100%

the highest implied utilization = 113.33%

the arrival rate will not be equal to the actual flow rate for the customers.

So,

The actual flow rates for the sandwich-only customers = Arrival rate / The highest implied utilization

The actual flow rates for the sandwich-only customers = 8 / 113.33%

The actual flow rates = 7.1 customers per hr.

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