Final answer:
The utilization rate of the servers at Shoprite's checkout area is approximately 37.5%, calculated by dividing the customer arrival rate of 20 customers/hour by the combined processing capacity of 53.33 customers/hour for all 8 servers and converting it to a percentage.
Step-by-step explanation:
The question asks about the utilization rate of servers at a checkout area in Shoprite where customers arrive at a certain rate and have an average processing time. To determine the utilization rate, we need to calculate the rate of customer arrivals and the average processing time per server.
Given that customers arrive at the rate of 20 customers per hour, this means on average, a customer arrives every 3 minutes (60 minutes / 20 customers = 3 minutes). With processing time reported as 9 minutes per customer and 8 servers available, we can determine the processing capacity per hour for all servers combined is 8 servers × (60 minutes / 9 minutes per customer) = about 53.33 customers per hour.
The utilization rate is then found by dividing the arrival rate by the combined service rate and expressing it as a percentage. Thus, the utilization rate is (20 customers/hour) / (53.33 customers/hour) × 100% ~ 37.5%. This represents the percentage of time that the servers are actively processing customers.