Answer
The problem is a classic “minimum‑cost path” in a directed graph.
The graph is very small, so the shortest‑path can be found by hand.
1 → 2 (cost 4)
2 → 3 (cost 4)
3 → 4 (cost 4)
4 → 5 (cost 4)
5 → 6 (cost 4)
6 → 7 (cost 4)
7 → 8 (cost 4)
8 → 9 (cost 4)
9 → 10(cost 4)
The total cost of this path is
4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 36
No other path can use fewer than nine edges, and every edge has a cost of at least 4, so 36 is the minimum possible.
Minimum cost = 36