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 $(13$ minutes$).$

Activity $2$: Wash and condition hair $(13$ minutes$).$

Activity $3$: Neck, shoulder, and back stress$-$release massage $(13$ minutes$).$

Activity $4$: Design the hairstyle and do the hair $(27$ minutes$).$

Activity $5$: Check out the guest $(10$ minutes$).$

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