Consider the following routing network, in which the amount of traffic to be sent from the source vertex s to the destination vertex t is 10 , and the expressions that label edges are their latency functions (where variable x denotes the argument of the latency function). (a) [10 marks ] Find a Wardrop equilibrium. (b) [10 marks] Calculate the price of anarchy. A routing network like above is a directed graph (V,E), with an edge latency function e for each edge eE, source-destination pairs (si,ti) for i=1,2,,k, and demands ri>0 for i=1,2,,k. Each such routing network can be interpreted as a non-atomic routing game or as an atomic routing game. For the latter interpretation, in which the flows on all paths are restricted to be non-negative integers, consider the following formalization of an equilibrium flow. We say that an integral flow f:PZ0 is an atomic Wardrop equilibrium if for all i=1,2,,k, and for all source-destination paths p,pPi from si to ti, we have: if f(p)>0 then p(f)p(f) where f(q)=f(q)1f(q)f(q)+1ifq=pifq=pandq=pifq=p (c) [10 marks ] Find all the atomic Wardrop equilibria in the routing network above. (d) [5 marks] Calculate the largest social cost of an atomic Wardrop equilibrium