Consider your typical sandwich shop $($an example would be Subway$).$ We are interested in modeling the operations of such a shop. Customers typically arrive to this system following a particular distribution. There are usually about five $(5)$ stations in the system. The first station $("$Bread$,$ Meat & Cheese" or $"$BMC$")$ is where the customer selects their choice of bread, meat and cheese products. Once completed, the customer has the choice of whether to have the bread toasted or not. An oven station is available if the bread needs to be toasted. The process then proceeds to the "Veggies" station where customer selects from Veggie options available, Next is the "Cashier" station, where payment is made and finally, customers grab a drink at the "Drink" station on their way out.

The following information is provided for the arrival and service processes;

The arrival process is exponentially distributed with an arrival rate of $30$ customers per hour

The service times are all exponentially distributed with the following service times in minutes:

BMC Station: $1\mathrm{.}25$

$>$ Oven Station: $2$

We assume that the oven has a capacity of one. Only one sandwich is toasted per time

$>$ Veggie Station: $1\mathrm{.}5$

$>$ Cashier Station: $1$

$>$ Drink Station: $1\mathrm{.}25$

$65\%$ of the customers want their sandwich toasted, while the remaining $35\%$ get cold sandwiches $($i$.$e$.$ not toasted$)$

a$)$ Evaluate the performance of the system using the following performance measures at steady state conditions:

i$.$ Server Utilizations

ii$.$ Average Time in System

iii. Expected Number in System

b$)$ Introduce a Status Plot feature to your model and use it to capture the "Number of Customers" in the system and the "Average Number of Customers" in the system. Use a $12hr$ interval for your analysis.