Q$1)(50$ points$)$

Use Dijktras Algorithm for determining the shortest path $($from node O to node T $)$ for the following network.

Q$2)(50$ points$)$

For the network shown below, use Ford$-$Fulkerson algorithm described in class to find the flow pattern giving the maximum flow from the source to the sink, given that the arc capacity from node $i$ to node $j$ is the number nearest node i along the arc between these nodes. Show your work for each iteration of the algorithm.