$19\mathrm{.}11$ Workstations, servers, cycle times, and station workloads for an FMS with three processing

stations are listed in the table below. The FMS produces $4$ parts. Other stations are load$/$

unload $($station $4,2$ servers$),$ transport $($station $5,1$ shuttle cart$),$ and station $6($storage$,30$

spaces$).$ Station $4$ loading and unloading times are before and after the slash. Station $5$ travel

loaded and travel empty times are before and after the slash. Parts loaded into the FMS at

station $4$ are shuttled to station $6$ before beginning their respective process routings. When

processing is completed, parts are moved back to storage and then to unload when station

$4$ is available. Solve for the overall production rates, manufacturing lead times, waiting

times, and station utilizations, given the following number of parts in the system: $($a$)N=1,$

$($b$)N=5,$ and $($b$)N=12.$