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A flexible manufacturing system (FMS) is being planned. It has a network diagram pictured in following Figure and uses a automated guided vehicle (AGV) system to move parts between stations in the network. All work parts are loaded into the system at station 1 , moved to one of three processing stations (2,3, or 4), and then brought back to station 1 for unloading. Once loaded onto its AGV, each work part stays onboard the vehicle throughout its time in the FMS. Load and unload times at station 1 are each 1.0min. Processing times at other stations are: 5.0min at station 2, 7.0min at station 3 , and 9.0min at station 4 . Hourly production of parts through the system is: 7 parts through station 2, 6 parts through station 3 , and 5 parts through station 4 . The figure shows that relationship between the stations and deliveries per hour between stations (above the slash) and distances in meters between stations (below the slash). Determine the number of automated guided vehicles that are needed to meet the requirements of the flexible manufacturing system, if vehicle speed =60m/min and the anticipated traffic factor =0.85. Assume reliability =100%