$(15$ points$)$ Mr$.$ K$\text{'}$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 $(11$ minutes$).$

Activity $2$: Wash and condition hair $(11$ minutes$).$

Activity $3$: Neck, shoulder, and back stress$-$release massage $(11$ minutes$).$

Activity $4$: Design the hairstyle and do the hair $(24$ minutes$).$

Activity $5$: Check out the guest $(7$ 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 $5$

a$.$ What is the labor content?

b$.$ What is the average labor utilization?

Note: Round your final answer to two decimal places.

c$.$ At a wage rate of $$21$ per hour, what is the cost of direct labor per customer? Note: Round your final answer to two decimal places.

d$.$ Mr$.$ K considers hiring a new employee to help any one $($and only one$)$ of the servers without changing the tasks performed by each server. What will be the new cost of direct labor?

Note: Round your final answer to two decimal places.

e$.$ Returning to the three$-$worker scenario, Mr$.$ K contemplates redesigning the assignment of tasks to servers. For this, Mr$.K$ is evaluating the reassignment of Activity $5$ from S$3$ to S$1.$ What will be the new cost of direct labor? Note: Round your final answer to two decimal places.