a$)$ Consider the maximum flow problem from node $1$ to node $6$ on the network given above. On each arc we have two numbers in the form $(x$;$y).$ The first number $x$ shows the capacity of the arc and $y$ shows the current flow on the arc.

i$)$ What is the value of the current flow?

ii$)$ What is the value of the maximum flow? Indicate the value of flow on each arc for the optimal solution.

b$)$ Suppose you have a network that consists of $100$ nodes. You would like to find the shortest path from node $1$ to node $100$ that does not go through node $49.$ How would you solve this problem?