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 $(10$ minutes$).$

Activity $2$: Wash and condition hair $(10$ minutes$).$

Activity $3$: Neck, shoulder, and back stress$-$release massage $(10$ minutes$).$

Activity $4$: Design the hairstyle and do the hair $(25$ 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 $5.$

a$.$ What is the labor content?

b$.$ What is the average labor utilization?

c$.$ At a wage rate of $$20$ per hour, what is the cost of direct labor per customer?

d$.$ Mr$.$ K considers hiring a new employee to help any one $($and only one$)$ of the service employees without changing the tasks performed by each service employee. How would this change his cost of direct labor?

e$.$ Mr$.$ K also contemplates redesigning the assignment of tasks to service employees. For this, Mr$.$ K is evaluating the reassignment of activity $5$ from S$3$ to S$1.$ How would this change his cost of direct labor?