Circular blanks are loaded into a deep drawing machine by an automatic loading and unloading mechanism. The loading and unloading task takes $20$ sec each cycle. The drawing operation itself takes $10$ sec$,$ including part ejection. The cost rates of the drawing machine and the automatic loading and unloading mechanism are $$45/$hr and $$10/$hr respectively. The drawing die cost $$12,000$ and is expected to produce a total number of drawn parts equal to the first$-$right five digits of your student number during its life. Batch quantity is $1300$ parts. Time to set up the machine before production is $2$ hr$.$ Determine: $($a$)$ Time to complete the batch $($b$)$ Average production rate, $($c$)$ Cost per piece