A FMS consists of three stations plus a load/unload station. Station 1 loads and unloads parts using two servers (material handling workers). Station 2 performs horizontal milling operations with two servers (identical CNC horizontal milling machines). Station 3 performs vertical milling operations with three servers (identical CNC vertical milling machines). Station 4 performs drilling operations with two servers (identical drill presses). The machines are connected by a part handling system that has two work carriers and a mean transport time = 3.5 min. The FMS produces four parts, A, B, C, and D, whose part mix fractions and process routings are presented in the table below. The operation frequency fijk = 1.0 for all operations. Determine
(a) Maximum production rate of the FMS,
(b) Utilization of each machine in this system, and

min in mi min in in in in es 4 15 4 3 342 16 1 1 34 10 9 34 18 8 3 ti-1 2 3 4 1-1 4 2 3 4 11241-1341 1 2 3 4 5|1 2 3 4 5 6 1 2 3 4|1234