Consider the scenario shown below, with four different servers connected to four different clients over four three$-$hop paths. The four pairs share a common middle hop with a transmission capacity of R $=400$ Mbps$.$ The four links from the servers to the shared link have a transmission capacity of RS $=50$ Mbps$.$ Each of the four links from the shared middle link to a client has a transmission capacity of RC $=20$ Mbps$.$

$1.$ What is the maximum achievable end$-$end throughput $($in Mbps$)$ for each of four client$-$to$-$server pairs, if the middle link divides its transmission rate equally?

$2.$ Which link is the bottleneck link?

$3.$ Assuming that the servers are sending at the maximum rate possible, what is the link utilizations for the shared link $($R$)?$