$($A$)$ A job shop has three workstations, each with multiple servers. It operates $80$ hours per week and produces four different product styles: A$,$ B$,$ C$,$ and D$.$ Part$-$mix ratios, batch quantities, part routings, machines, servers, and production times are given in the table below for the four product styles made in the shop. Operation sequence for product style is in the order of station number. Determine $($a$)$ which station is the bottleneck, $($b$)$ total weekly output of all four products, $($c$)$ weekly output of each of the four product styles, $($d$)$ utilization of each server at each station, $($e$)$ average utilization of the machine shop. Setup times are accounted for in the $T_p$ values.

$\backslash$table$[[$Part style $(j),$A$,$B$,$C$,$D$,],[$Part mix $p_i,0\mathrm{.}24,0\mathrm{.}18,0\mathrm{.}31,0\mathrm{.}27],[$Batch quantities $Q_b,15,20,10,12],[$Stations $(i),$Servers $s_i,T_{pA}(hr),T_{pB}(hr),T_{pC}(hr),$