A ten$-$station assembly machine has an ideal cycle time of $4sec.$ Assume that defects never jam the workstations. When a breakdown occurs, it takes $1\mathrm{.}5$ min, on average, for the system to be put back into operation. Determine:

$($a$)$ the hourly production rate for the assembly machine,

$($b$)$ yield of good product $($final assemblies containing no defective components$),$ and

$($c$)$ proportion uptime of the system