Problem #$4(20$ points$)$

The table below lists stations, servers, cycle times, and station workloads for an FMS with four processing stations that produce four products. Additional stations are load$/$unload $($station $5,2$ servers$),$ transport $($station $6,1$ shuttle cart$),$ and station $7($storage$,10$ spaces$).$ Station $5$ loading and unloading times are before and after the slash. Station $6$ traveling loaded and traveling empty times are before and after the slash. For every transport move, there is an empty move. The parts are transported on pallet fixtures from station $5$ to part$-$storage station $7,$ from which they are moved through their respective process routings, then back to storage, and finally to unloading at station $5.$ Determine $($a$)$ bottleneck station, $($b$)$ total hourly output of the system, $($c$)$ number of busy servers at each station, $($d$)$ utilization of each server, and $($e$)$ average utilization of the processing stations.

$\backslash$table$[[$Part Style $($j$),$A$,$B$,$C$,$D$],[$Part$-$mix fraction $p_j,0\mathrm{.}25,0\mathrm{.}35,0\mathrm{.}2,0\mathrm{.}2,],[\backslash$table$[[$Station$],[($i$)]],$Operation,$\backslash$table$[[$Servers$],[s_i$