A work cell is required to make $210$ computerized diagnostic assemblies $($for installation into hybrid automobiles$)$ each day. The cell currently works an eight hour shift, of which seven hours is available for productive work. These assemblies require five operations. Standard times for these operations are: Operation A$,1\mathrm{.}5$ minutes, B$,1\mathrm{.}8$ minutes, C$,2\mathrm{.}4$ minutes, D$,2\mathrm{.}5$ minutes, and E$,1\mathrm{.}4$ minutes.

$($a$)$ What is takt time for this cell?

$($b$)$ How many workers are required for this cell?

$($c$)$ What is the actual output of this cell?