Leif's Website

The input is small enough that brute-forcing is doable, but a best-first search would likely be faster.

input = Import@"input.txt"

lines = ToExpression@
   StringCases[StringSplit[input, "\n"], 
    NumberString | (CharacterRange["A", "Z"] ~~ 
       CharacterRange["A", "Z"])];
flow = Select[AssociationThread @@ Transpose@lines[[;; , 1 ;; 2]], 
   Positive];
d = With[{g = Graph@Flatten[Thread[#[[1]] -> #[[3 ;;]]] & /@ lines]}, 
   AssociationThread[
    VertexList@
      g -> (AssociationThread[VertexList@g -> #] & /@ 
       GraphDistanceMatrix@g)]];
f[closed_, from_, minutes_] := 
 f[closed, from, minutes] = 
  Max[0, With[{remaining = minutes - d[from, closed[[#]]] - 1}, 
      If[remaining > 0, 
       flow[closed[[#]]]*remaining + 
        f[Delete[closed, #], closed[[#]], remaining], Nothing]] & /@ 
    Range@Length@closed]
f[{}, _, _] = 0;

f[Keys@flow, AA, 30]
Max[f[#, AA, 26] + f[Complement[Keys@flow, #], AA, 26] & /@ 
  Subsets@Keys@flow]