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]

Functions in Mathematica are symbolic expressions you can examine and modify just like any other symbolic expressions, which allows for some fun:

i=Import@"input.txt";
{items,inspect,throw}=Association/@Transpose[Thread[#[[1,1]]->{#[[2]],(x|->a[x,b])/.{a->#[[3,1]],b->If[Length@#[[3]]>1,#[[3,2]],x]},(x|->If[Divisible[x,a],b,c])/.{a->#[[4,1]],b->#[[5,1]],c->#[[6,1]]}}]&@ToExpression[StringSplit[#,Except[DigitCharacter|"*"|"+"]..]/.{"+"->Plus,"*"->Times}]&/@StringSplit[StringSplit[i,"\n\n"],"\n"]];
Times@@TakeLargest[Merge[Reap[Fold[Merge[{Append[#1,#2->{}],Sow[#2->Length@#1@#2];With[{items=Mod[inspect@#2/@#1@#2,LCM@@throw[[;;,2,1,2]]]},Thread[throw@#2/@items->items]]},Flatten]&,items,Flatten@Table[Keys@items,20]]][[2,1]],Total],2]