solve it step by step, and dont copy and paste from other solution.

Part j ABCD 19.16 A flexible manufacturing cell consists of a manual load/unload station, three CNC machines, and an automated guided vehicle system (AGVS) with two vehicles. The vehicles deliver parts to the individual machines, drop off the parts, and then go per- form other work. The workstations are listed in the table below, where the AGVS is station 5. Station Description Servers 1 Load and unload 1 worker 2 Milling 1 CNC milling machine 3 Drilling 1 CNC drill press 4 Grinding 1 CNC grinding machine 2 vehicles 5 AGVS The FMC is used to machine four parts. The product mix, routings, and processing times for the parts are presented in the table below: Part Mix pj Station Routing Station 1 Station 2 Station 3 Station 1 1-2-3-4-1 4 min 8 min 0.25 0.33 2 min Station 4 18 min 0 14 min 7 min 10 min 1-3-2-1 4 min 9 min 2 min 0.12 1-2-4-1 4 min 10 min 2 min 0 12 min. 0.30 1-2-4-3-1 4 min 6 min 16 min 2 min The mean travel time of the AGVS between any two stations in the FMC is 3.0 min, which includes the time required to transfer loads to and from the stations. Given that the load- ing on the system is maintained at 8 parts (8 work parts in the system at all times), use the extended bottleneck model to determine (a) the bottleneck station, (b) hourly production rate of the system (c) average time to complete a part and average waiting time, and (d) the average utilization of the regular stations in the system, not including the AGVS. A spreadsheet calculator is recommended for this