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Representation of time expanded graph

I want to build a time expanded graph with time discretization Dt that starts at t = 0 and ends at t = T where between the node (n1, t) and the node (n2, t') is an arc if and only if (n1, n2) were ...
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Dynamic programming proof

I have aquestion, lets say im trying to maximize: S=∑j=1nfj(xj) subject to ∑j=1nxj≤B, where B∈ℤ+ and fj:ℝ→ℝ. how would i do this using dynamic programming and what would be the states and ...