A proposed production system consists of several serial automatic workstations. A part circulates through the system. The part arrival rate is exponential with a mean of 10 for part 1. The part is processed at the first workstation with a TRIA(10,11,13) distribution. Then the part is inspected. It has an inspection time of UNIF(2,6). The part is inspected, it has a 70% success rate the first time it is processed and a 95% success rate the second time. However, if the part fails the second time, it is scrapped. The passed parts then go through a painting process with a constant time of 10. After the painting, the part is packaged by the same person who paints the part and has a rate of NORM(11,2). If the part has only been processed 1 time, it is considered a Tier 1 product, if it has been processed 2 times it is considered a Tier 2 product. Tier 1 products have an additional processing step, before they are shipped. This step includes premier packaging and has a rate of Constant(3). All times are given in minutes. This system works three 3-hour shifts with two operators at Workstation 1. There is only 1 inspector. Then a single worker performs both the painting and regular packaging process. Then another worker conducts the premium packaging. The operators work so that if the workstation has 2 operators, they stagger their breaks and have 10 minute breaks between shifts. If the workstation has only 1 operator, they take their break at the beginning of the next shift. All operators finish the task they are working on before leaving for their break. Please use one instance of Route and Station at least.

a) What is the average cycle time (system time)?

b) What is the highest average queue length?

c) What is the maximum number of times a part is processed at workstation 1?

Please provide step-by-step full solution using Arena model with the model and answers for a, b and c