Consider the Jackson Network given in the figure below. There are three stations, each of which is an M$/$M$/$c system. The service rate of server in each station is given such that $\backslash$mu i denotes the service rate of a server in station i$.$ Also, the numbers next to the arcs represent the probability of a customer choosing the arc. a$)(0\mathrm{.}5)$ Calculate the minimum number of servers needed in Station $1$ for feasibility. b$)(1\mathrm{.}5$ point$)$ Calculate the arrival rate in station $2$ and then calculate the minimum number of servers needed in Station $2$ for feasibility. Show your calculations. c$)(1\mathrm{.}5$ point$)$ Calculate the arrival rate in station $3$ and then calculate the minimum number of servers needed in Station $3$ for feasibility. Show your calculations. d$)(2$ point$)$ Using the key performance measures for each station from the templates, calculate the expected total number of customers in the network and expected amount of time a customer spends in the queue.