$3\mathrm{.}15$

A machine shop has four machines of five different types and operates $40$ hours per week. Part$-$mix ratios, batch quantities, part routings, machines, servers, and production times are given in the table below for the five part styles produced in the shop. Operation sequence for each part style is in the order of station number. Part styles are identified by letter and stations are identified by number. Determine $($a$)$ which station is the bottleneck, $($b$)$ total production rate of all five parts, $($c$)$ production rates of each of the five part styles, $($d$)$ utilization of each server at each station, and $($e$)$ average utilization of the machine shop.

$\backslash$table$[[$Part style $(j),$A$,$B$,C,D,E$