A driver can travel on the streets shown on this map where costs of sub$-$paths are given.

Note that s$/$he can only drive following the directions of the arrows. Find the optimum path

$($minimum cost$)$ from start $($A$)$ to target $($P$)$ by using dynamical programing and back$-$

propagation, show both the path and its length $($trial & error solutions will not be accepted$)$