Question $4.$ Mr$.$ Bean's is a very popular hair salon. It offers high$-$quality hair$-$styling 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 below. $($The time required for each activity is shown in parenthesis$)$:

Activity $1$: Welcome a guest and offer homemade herb tea. $(10$ minutes$)$

Activity $2$: Wash hair. $(15$ minutes$)$

Activity $3$: Condition hair. Neck, shoulder, and back stress release massage. $(20$ minutes$)$

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

Activity $5$ : Check out the guest. $(5$ 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 $1$ and Activity $2.$

S$2$ does Activity $3.$

S$3$ does Activities $4$ and Activity $5.$

a$)$ What is the flow rate of the process and the average labor utilization of the servers? Assume the process operates at its capacity.

b$)$ Assume a wage rate of $$18$ per hour. What is the cost of direct labor?

c$)$ To increase the service rate, Mr$.$ Bean's is considering two alternatives:

Alternative $1$: To hire a new employee to help any $($and only one$)$ of the servers without changing the tasks performed by each server.

Alternative II: To redesign the assignment of tasks to servers. For this, Mr$.$ Bean's is evaluating to reassign Activity $5$ from S$3$ to S$1.$

Which alternative do you think will be better? Analyze it in Excel and come up with a conclusion.