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

Task time

Task $115$ min

Task $28$ min

Task $317$ min

Task $420$ min

Task $56$ min

Task $624$ 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 $6.$