Customers arrive to Crystal River Day Spa and request combinations of two different types of treatments: $1)$ massage; $2)$ facial. Assume that these are the only two types of treatments offered by the day spa.

The overall demand rate is $114$ customers per day.

All customers must first check$-$in at reception which takes on average $9$ minutes.

$25\%$ of customers request a long massage whereas $20\%$ of customers request a short massage. The remaining customers wish to only receive a facial.

The long massage lasts $105$ minutes on average; whereas the short massage lasts $50$ minutes on average.

In both cases this includes the time for the massage therapist to prep the room, give the massage, and clean the room.

On average, $30\%$ of the customers that request a long massage also request a facial and $80\%$ of the customers who request a short massage also request a facial.

Facials are performed by an esthetician and take on average $75$ minutes regardless of whether the customer received a massage.

The day spa has $2$ receptionists, $5$ massage therapists, and $8$ estheticians working at any time during its $12-$hour workday, and at least that many rooms are available for each type of service. The price for a long massage is $$135,$ the price for a short massage is $$65,$ and the price for a facial is $$75.$

Rounding instructions.

Carry all calculations.

Enter all answers rounded to one decimal place.

Enter utilization as a percentage between $0$ and $100($e$.$g$.0\mathrm{.}4152$ should be entered as $41\mathrm{.}5\%).$

Hint: Use five flow$-$unit types to solve all parts of this problem.

a$.$ Compute the process capacity in incoming customers per day:

incoming customers per day.

b$.$ Compute the utilization of the massage therapists:

$\%$

c$.$ Compute the flow rate of customers who receive a short massage and a facial:

customers per day.

d$.$ Compute the average total revenue per day. $

per day.