The average part produced in a certain batch manufacturing plant must be processed se$.$ quechely through an average of tea operations. Twenty$-$five new batches of parts are launched each week. Average operation time is $10$ min, average setup time is $7\mathrm{.}5$ hr$,$ averise batch size is $20$ paris, and atiorage nonoperation time per batch is $12$ hr per i bathe. There are $25$ machines in the plant. Any machine can be set up for any type of batch processed in the plant. The plan operates $75$ production hr$/$wk$.$ Determine $($a$)$ perafacturing lead time for an average part, $($b$)$ plant capacity if all machines could be operated at $100\%$ utilization, $($c$)$ plant utilization, and $($d$)$ work$-$in$-$process $($number of plant utilization?

pars$-$in$-$process$).$