$19\mathrm{.}11$ 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$)N=12.$

$\backslash$table$[[$Part Style $($j$),$A$,$B$,C,$D$,],[$Part Mix $p_j,0\mathrm{.}15,0\mathrm{.}25,0\mathrm{.}35,0\mathrm{.}25,],[\backslash$table$[[$Stations$],[($i$)]],\backslash$table$[[$Servers$],[q,s_i$