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At the security station of Concourse A of Rochester's airport (ROC), all carry on bags must be first X-rayed. Two resources are involved in X-raying. First, there is a conveyor belt that moves the bags through the X-ray machine. The conveyor belt can hold at most 5 bags and it takes 25 seconds for a bag to travel from the beginning to the end of the machine (as long as the belt is not stopped by an X-ray inspector. The second resource is the X-ray inspector, who examines a picture of the bag, while it is on the belt. Examining the picture tales an average of 4 seconds. At any time, the inspector can stop the belt, if he/she wants.After being X-rayed, most bags are given back to the passengers. However, 5% of the bags are selected for bomb testing. First a security agent wipes a special cloth on the luggage and puts the cloth into a 'sniffer' machine that detects chemicals that might be used to make a bomb. This "wiping and placing" takes 10 seconds. Then the sniffer tests the cloth. Testing does not require the attention of the security agent. Testing requires, on an average 80 seconds.
a) Suppose the arrival rate of the bags is increasing dramatically. What is the capacity of the process, in bags per minute?What is the bottleneck of the process?
b) New security rules require that more than 5% of the bags must be passed through the sniffer. How high can the percentage rise without affecting capacity of the process?
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