PA $4-4($Algo$)$ Mr$.$ K$\text{'}$s is a very popular hair salon. It$...$

Mr$.$ K$$s is a very popular hair salon. It offers high$-$quality hairstyling and physical relaxation services at a reasonable price, so it always has unlimited demand. The service process includes five activities that are conducted in the sequence described next $($the time required for each activity is shown in parentheses$)$:

Activity $1$: Welcome a guest and offer homemade herb tea $(9$ minutes$).$

Activity $2$: Wash and condition hair $(9$ minutes$).$

Activity $3$: Neck, shoulder, and back stress$-$release massage $(9$ minutes$).$

Activity $4$: Design the hairstyle and do the hair $(23$ minutes$).$

Activity $5$: Check out the guest $(5$ minutes$).$

Three service employees $($S$1,$ S$2,$ and S$3)$ offer the services in a worker$-$paced line. The assignment of tasks to the service employees is the following: S$1$ does activity $1,$ S$2$ does activities $2$ and $3,$ and S$3$ does activities $4$ and $5.$