$\mathrm{.}7($Car Wash Supply Process$)$ CC Car Wash specializes in car cleaning services. The ser$-$ vices offered by the company, the exact service time, and the resources needed for each of them are described in the table following:$53$ Understanding the Supply Process: Evaluating Process Capacity Resource Used $1$ automated washing machine $1$ automated waxing machine $1$ employee $1$ employee Service Description Processing Time A$.$ Wash Exterior car washing and drying $10$ min B$.$ Wax Exterior car waxing $10$ min C$.$ Wheel cleaning Detailed cleaning of all wheels D$.$ Interior cleaning Detailed cleaning inside the car The company offers the following packages to their customers $7$ min $20$ min Package $1$: Includes only car wash $($service A Package $2$: Includes car wash and waxing $($services A and B$)$ Package $3$: Car wash, waxing, and wheel cleaning $($services A$,$ B$,$ and C$)$ Package $4$: All four services $($A$,$ B$,$ C$,$ and D$)$ Customers of CC Car Wash visit the station at a constant rate $($you can ignore any effects $..$ of variability$)$ of $40$ customers per day. Of these customers, $40$ percent buy Package $115$ percent buy Package $2,15$ percent buy Package $3,$ and $30$ percent buy Package $4.$ The mix does not change over the course of the day. The store operates $12$ hours a day What is the implied utilization of the employee doing the wheel cleaning service? b$.$ Which resource has the highest implied utilization? For the next summer, CC Car Wash anticipates an increase in the demand to $80$ cus$-$ tomers per day. Together with this demand increase, there is expected to be a change in the mix of packages demanded: $30$ percent of the customers ask for Package $1,10$ percent for Package $2,10$ percent for Package $3,$ and $50$ percent for Package $4.$ The company will install an additional washing machine to do service A c$.$ What will be the new bottleneck in the process? d$.$ How many customers a day will not be served? Which customers are going to wait? Explain your reasoning!