Return to the problem of Exercise 9-1.

(a) Find (by inspection) shortest paths from node 1 to all other nodes.

(b) Verify that every subpath of the optimal 1 to 2 path in part

(a) is itself optimal.

(c) Detail your optimal solutions of part (a)

in functional notation n[k] and xi,j[k].

(d) Write functional equations for the shortest path problems of part (a).

(e) Verify that the n[k] of part

(c) satisfy functional equations of part (d).

(f) Explain why functional equations are sufficient to characterize optimal values n[k]

for this instance.