$1.$ Consider the following problem, based on a real$-$world problem. It is $2021$ and a medical clinic in Halifax wants to run a drive$-$through vaccination clinic. The vaccination clinic will run for $4$ hours and has a target throughput of $100$ cars.

A drive through clinic consists of four steps:

$1)$ Greeting $($met the vehicle, identify the occupants, and check off against a list$).$ Greeting takes, on average, $3$ minutes per car. You can assume that the greet function is exponentially distributed.

$2)$ Explanation and Consent $($a clinician explains the procedure, describes the vaccine to be administered, and obtains written consent for each person in the car over the age of $16).$ This function takes $4$ minutes per car, on average. Again, you may assume an exponential service time.

$3)$ Vaccine administration $($a clinical person administers the vaccine to all persons in the car$).$ This activity requires $5$ minutes, exponentially distributed.

$4)$ Post$-$vaccine hold. Cars are required to wait $15$ minutes before leaving, to ensure that no one in the vehicle has an adverse reaction. You can assume that the $15$ minutes wait is exponentially distributed $($for simplicity$).$