Question $2$: $(20$ Marks$)$

A high$-$production operation was studied during an $80-$hr period. During that time, a total of seven equipment breakdowns occurred for a total lost production time of $3\mathrm{.}8hr,$ and the operation produced $38$ defective products. No setups were performed during the period. The operation cycle consists of a processing time of $2\mathrm{.}14$min, a part handling time of $0\mathrm{.}65$min, and a tool change is required every $25$ parts, which takes $1\mathrm{.}50$min.

Determine:

$($a$)$ hourly production rate of acceptable parts

$($b$)$ scrap rate during the period.