Cynthya is a big fan of the band Suplaz, which rarely performs in Brazil. She just found out they’ll be at Rock in Rio festival and is thrilled. She is the manager of the Capanema Suplaz fan group, so she decides to organize transportation to help as many fans as possible from her city attend the concert.
Since the trip is long, she sets up a system of shared rides and transfers: fans can travel between cities using different cars, vans, or buses, meeting at stops along the way. At each segment of the trip, there is a limit to how many people can be transported, depending on vehicle availability. Fans may switch vehicles at intermediate stops.
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The figure above represents this transportation system as a directed network. Capanema is the source (S) and Rio is the sink (T). The intermediate nodes (A, B, C, and D) represent transfer points, like hotels or meeting locations. Each edge has a capacity, indicating the maximum number of people that can travel along that segment.
What is the maximum flow from Capanema to Rio, which corresponds to the maximum number of fans that can be transported?
A) 8
B) 10
C) 20
D) 12
E) None of the above
Original idea by: Melissa Araújo
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