Question 1. Items arrive at a single machine system according to an exponential interarrival distribution with a mean of 20 minutes; the first part arrives at time 0. Upon arrival, the parts are processed at a machine. The processing-time of the machine has triangle distribution with parameters (11, 16, 18) in minutes. The parts are inspected and there is a 0.24 probability for each part that it will need to be sent back to the same machine to be reprocessed. Run the simulation for a single replication of length 20,000 minutes to collect statistics and the average part cycle time (time from a parts entry to the system to its exit).

Please calculate the below statistics in minutes: a) Average number of items in the system .......... b) Average number of items in queue .......... c) Average utilization of the machine .......... d) Average cycle time ........... e) Average waiting time in the queue per item ............ f) Average processing time in the machine ........... g) Total number of items that started service ............ h) Total number of items that processed in the machine ............ i) Total number of items that left the system .......... j) Total number of items failed the inspection .............