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Transportation Problems

A railroad network serving six major Canadian cities, with the daily number of car compartments.

    
Wolfram Language code: g = [image];
Find the maximum number of compartments that can be carried from Vancouver to Winnipeg:
Wolfram Language code: ℱ = FindMaximumFlow[g, "Vancouver", "Winnipeg", "OptimumFlowData"];
Wolfram Language code: ℱ["FlowValue"]
Number of compartments between cities:
Wolfram Language code: Text[Grid[{#, ℱ[#]}& /@ ℱ["EdgeList"], Background -> {None, {{White, Lighter[Blend[{Blue, Green}], .8]}}}, Dividers -> All, Alignment -> {{Center, Right}}, ItemSize -> {{17, 6}}, Frame -> Darker[Gray, .6], ItemStyle -> 14, Spacings -> {Automatic, .8}]]
Show the flows of compartments:
Wolfram Language code: Panel[Show[{CountryData["Canada", "Shape"], ℱ["FlowGraph"]}, PlotRange -> {{-0.31, 0.083}, {0.04, 0.25}}]]