An assembly$-$line process has six tasks, as listed in the table below:

Task time $15$ min

$8$ min

$17$ min $20$ min

$6$ min

$24$ min

Four workers $($S$1,$ S$2,$ S$3,$ and S$4)$ are staffed to this assembly line, and the assignment of tasks to each

worker is as follows:

$$ S$1$ does Task $1.$

$$ S$2$ does Tasks $2$ and $3.$

$$ S$3$ does Tasks $4.$

$$ S$4$ does Tasks $5$ and $6.$

For the following questions, we assume that the process is operating at full capacity.

$($a$)$ Whichworkeristhebottleneckoftheprocess?Whatistheprocesscapacityin$[$units$/$hour$]?(1$ point$)$

$($b$)$ Whatistheidletimeofeachworkerin$[$minutes$]?$

$($c$)$ Assume a wage rate of $$18$ per hour. What is the direct labor cost in $[$$$/$unit$]?$

$($d$)$ Still assume a wage rate of $$18$ per hour. If we reassign Activity $5$ from S$4$ to S$3,$ what will be the new direct labor cost in $[$$$/$unit$]?$ Is this reassignment an improvement? $($keep $2$ decimals$)$