$1\mathrm{.}4-2$ Maximum end$-$end throughput. Consider the scenario shown below, with $10$ different servers $($four shown$)$ connected to $10$ different clients over ten three$-$hop paths. The pairs share a common middle hop with a transmission capacity of R $=200$ Mbps$.$ Each link from a server has to the shared link has a transmission capacity of RS $=25$ Mbps$.$ Each link from the shared middle link to a client has a transmission capacity of RC $=50$ Mbps$.$