$2\mathrm{.}72\mathrm{.}7.$ The average part produced in a certain batch manufacturing plant must be processed

through an average six machines. Twenty $(20)$ new batches of parts are launched each

week. Average operation time $=6$min., average setup time $=5$ hours, average batch size $=$

$25$ parts, and average nonoperation time per batch $=10h\frac{r}{?}$ machine. There are $18$

machines in the plant. The plant operates an average of $70$ production hours per week.

Scrap rate is negligible. Determine: $($a$)$ manufacturing lead time for an average part, $($b$)$

plant capacity, $($c$)$ plant utilization. $($d$)$ How would you expect the nonoperation time to be

affected by the plant utilization?