$3\mathrm{.}18($A$)$ A batch of parts is routed through six machines in a batch production plant. Batch size is $100.$ At each machn e$,$ the parts are processed sequentially. Setup times and cycle times are given in the table below. Average nonoperation time per machine is $12hr.$ Determine the $($a$)$ manufacturing lead time and $($b$)$ hourly production rate for operation $3.$