An NC worktable is driven by a close loop positioning system consisting of a servomotor, ball screw, and optical encoder. The screw has a pitch $=6\mathrm{.}0$mm and is coupled to the motor shaft with a gear ratio of $5$:$1($five turns of the motor for each turn of the screw$).$ The optical encoder generates $120$ pulses$/$rev of the screw. The table has been programmed to move $80\mathrm{.}00$ mm at a feed rate of $300$ mm$/$min$.$

Determine

$($a$)$ how many pulses are received by the control system to verify that the table has moved exactly $80.$mm; and

$($b$)$ the pulse rate, and

$($c$)$ motor speed that correspond to the specific feed rate.