A three$-$station dial$-$indexing machine assembles components to a base part. The operations, element times, $q$ and $m$ values for components added are given in the table below $($NA means $q$ and $m$ are not applicable to the operation$).$ The indexing time is $2$ sec $.$ When a jam occurs, it requires $1\mathrm{.}5$ min to release the jam and put the machine back in operation. Determine $($a$)$ hourly production rate for the assembly machine, $($b$)$ yield of good product $($final assemblies cont$$ining no defective components$),$ and $($c$)$ proportion uptime of the system.