Two family doctors have a clinic $($i$.$e$.,$ they share office space$)$ and each one has his$/$her own assistant. The family doctors are considering pooling their assistants to gain efficiency in the clinic operations. Currently, a task is given to an assistant, on average, once every $25$ minutes. It takes an assistant an average of $20$ minutes to complete a task. On the basis of available data, assume that both task inter$-$arrival times and task durations follow exponential distributions.$$

Consider parts a$)$ and b$)$ below a queueing theory exercise. Consequently, use the corresponding versions of the PK formula discussed in class.$$

a$)$ What effect will the pooling of assistants have on task waiting times and assistants$$ utilization? Show your computations.$$

b$)$ Based on your results from part a$),$ do you think the doctors should pool their assistants? Explain your answer.$$

c$)$ What advantages and disadvantages, other than those emphasized in part b$),$ are to be gained from pooling assistants? Explain at least one advantage and one disadvantage.$$

d$)$ Would you consider Queueing Theory an appropriate methodology to study this setti