A$-$ Re$-$circulating conveyor has a total length of $150$ m $.$ Its speed is $30\frac{m}{m}in$ and the spacing of part carriers along its length is $7\mathrm{.}5$ m $.$ Each carrier can hold two parts. Robots are used to load and unload the conveyor at its load and unload stations. The time required to load a part is $0\mathrm{.}20$ min and the unload time is the same. The required loading and unloading rates are both $1\mathrm{.}0$ part$/$min$.($a$)$ What is the maximum possible flow rate of parts on the conveyor system?

$($b$)$ How many parts could be contained on the conveyor system if every carrier were filled to capacity?

$($c$)$ How much time is required for the conveyor to make one complete loop?