Longest Path in a acyclic, directed graph

Question

Is there a known algorithm which finds the longest path in an acyclic, directed graph like the one below?

For this example, the algorithm should calculcate a longest path of 28m

Answer 1

Hint:

• Use dynamic programming on the partial order implied by the graph.
• To simplfy, you can first order the graph topologically.

I hope this helps $\ddot\smile$