Question $6(25$ points$)$

A Health Center at a local community is considering setting up a clinic office operated by one

employee to provide Influenza $($flu$)$ vaccines. Based upon information obtained from similar

clinics, it is believed that faculty or students will arrive at the office at a rate of $5$ per hour. It takes

an average of $10$ minutes to have a vaccine. It is assumed that the arrivals follow a Poisson

distribution and answer times are exponentially distributed.

a$)$ Find the proportion of the time that the employee is idle. $(5$ points$)$

b$)$ Find the average number of people receiving and waiting to receive vaccine. $(5$ points$)$

c$)$ Find the average time a person seeking vaccination spends in the system. $(5$ points$)$

d$)$ Suppose that the cost of waiting time is $$15$ per hour of time spent waiting in line. Find the

expected costs over an $8-$hour day. $(10$ points$)$