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 $=300$ Mbps$.$ The four links from the servers to the shared link have a transmission capacity of RS $=70$ Mbps$.$ Each of the four links from the shared middle link to a client has a transmission capacity of RC $=80$ Mbps$.1.$ What is the maximum achievable end$-$end throughput $($in Mbps$)$ for each of four client$-$to$-$server pairs, assuming that the middle link is fairly shared $($divides its transmission rate equally$)?$

$2.$ Which link is the bottleneck link? Format as Rc$,$ Rs$,$ or R

$3.$ Assuming that the servers are sending at the maximum rate possible, what are the link utilizations for the server links $($RS$)?$ Answer as a decimal

$4.$ Assuming that the servers are sending at the maximum rate possible, what are the link utilizations for the client links $($RC$)?$ Answer as a decimal

$5.$ Assuming that the servers are sending at the maximum rate possible, what is the link utilizations for the shared link $($R$)?$ Answer as a decimal