Problem $3$

Espresso Bean Inc. has hired you as their new manager. You notice the below count for each service provided in the coffee shop:

$\backslash$table$[[$Resource$,$Number$],[$Service Provided,Count$],[$Barista$,4],[$Espresso Machine,$3],[$Toaster$,2],[$Customer Parking,$55],[$Coffee Shop Capacity,$65]]$

Each car arrives with a group of $1\mathrm{.}5$ customers on average and each group stays $25$ minutes on average. The shop offers only espressos and bagels. $75\%$ of customers order an espresso while $60\%$ order a bagel. Each espresso machine can make an espresso in $5$ minutes while a toaster can toast $2$ bagels every $2$ minutes. A barista can take a customer order every $2$ minutes for each group $(1\mathrm{.}5$ customers on average per order$).$ Assume all bagels are toasted, and $2$ bagels are always toasted at a time.

a$.$ What is the capacity of each resource in customer$-$arrivals per hour?

b$.$ What is the system capacity in customer$-$arrivals per hour? Which resource$($s$)$ is $($are$)$ the bottleneck$($s$)?$

c$.$ What is the utilization of each resource? Please provide answers to the nearest percent.

d$.$ If you increase the number of units of the bottleneck resource$($s$)$ by one, what is the new system capacity in customer$-$arrivals per hour?