$3\mathrm{.}18($A$)$ A batch of parts is routed through six machines in a batch production plant. Batch size is $100.$ At each machine, 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 $3.$

$\backslash$table$[[$Machine$,1,2,3,4,5,6],[$Setup time $($hr$),4\mathrm{.}5,2\mathrm{.}0,5\mathrm{.}0,3\mathrm{.}0,2\mathrm{.}5,4\mathrm{.}0],[$Cycle time $($min$),5\mathrm{.}0,3\mathrm{.}5,6\mathrm{.}2,1\mathrm{.}9,4\mathrm{.}1,2\mathrm{.}5]]$