$1-$ Find the shortest path from node $1$ to $8$ in the following network:

a$)$ Using Acyclic Algorithm.

b$)$ Using Dijkstra's Algorithm.

c$)$ Assume that the arc between node $3$ and node $6$ is reversed $(c_{63}=4).$ Can we find the shortest

path using Acyclic Algorithm? If it is not possible explain in detail or find the shortest path.

d$)$ Assume now that the cost of arc between node $1$ and node $2$ is $3(c_{12}=3)$ and the cost of arc

between node $2$ and node $3$ is $-2(c_{23}=-2).$ Can we find the shortest path using Dijkstra's

Algorithm? If it is not possible explain in detail or find the shortest path.