A process has $3$ stages as shown. P$1,$ P$2,$ R$1,$ M$1,$ M$2,$ M$3$ are $6$ machines. The number in the box

$($besides the machine label$)$ is the machine capacity in $[$units$/$hour$].$

$($a$)$ What is the designed cycle time for stage $1($in $[$min$/$unit$])?$