Consider a production system consisting of three workstations $($w$/$s$)$ in series as illustrated below. The

routing for this part is w$/$s $1->$ w$/$s $2->$ w$/$s $3.$

$1.$ Historical data indicates the average defect rate at w$/$s$$s $1,2,$ and $3$ are $3\%,4\%,$ and $6\%,$

respectively. Assuming all defects must be scrapped, how many parts need to be started to achieve an

output of $1000$ parts?