Consider the scenario shown in Figure below in which a server is connected to the Router $1$ by a $100$ Mbps link with a $50$ms propagation delay. Initially Router $1$ is also connected to two routers $($Router $2$ and Router $3),$ each over a $50$ Mbps link with a $200$ms propagation delay. $1$Gbps links connect a host and a cache to each of these routers and we assume that the links between Router $2-$ Client$1,$ Router $2$ Cache $1,$ and Client $1-$ Cache $1$ have $0$ propagation delay. All packets in the network are $20,000$ bits long. $1.$ What is the end$-$to$-$end delay from when a packet is transmitted by the server to when it is received by Client $1?$ In this case, we assume there's no queuing delay at the routers, and the packet processing delays at routers and nodes are all $0.2.$ Here we assume that client hosts send requests for files directly to the server $($caches are not used or of in this case$).$ What is the maximum data rate at which Client $1$ can receive data from the server if we assume Client $2$ is not making requests? $3.$ Now we assume that the caches are ON and behave like HTTP caches. Again, Client$2$ is not active in this problem. Client$1\text{'}$s HTTP GET is always first directed to its local cache. $80\%$ of the requests can be satisfied by the local cache. What is the average data rate at which Client $1$ can receive a HTTP object in this case?