Please help and show all work!

Problem $1(20$ points$)$

Consider the acyclic network below:

$($a$)$ Label all of the nodes such that for every arc, $($i$,$j$),$ where i is the start and j the end node for the arc, the labels satisfy i $$ j

$($b$)$ Use forward DP to find the shortest path from node $1$ to all nodes in the network.