2. Suppose that we wanted to block access to the sea from inland town s on...

 

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2. Suppose that we wanted to block access to the sea from inland town s on a river. We can do this by dropping mines in the river, but because the river spreads out in a wide delta with several outlets, the number of mines required depends on where we drop them. The number of mines required in a channel range from a high of 20 to a low of 1 as shown by the network below. In that graph, each channel is shown with a number indicating how many mines will block it. a) What is the smallest number of mines needed to block off access from s to the sea (the sea is denoted by t), and where should the mines be placed? b) Give a mathematical argument that your answer is correct. S 20 a 6 6 2 C 5 4 3 6 10 5 f M 6 e 4 2 2 00 8 h 4 i 6 2. Suppose that we wanted to block access to the sea from inland town s on a river. We can do this by dropping mines in the river, but because the river spreads out in a wide delta with several outlets, the number of mines required depends on where we drop them. The number of mines required in a channel range from a high of 20 to a low of 1 as shown by the network below. In that graph, each channel is shown with a number indicating how many mines will block it. a) What is the smallest number of mines needed to block off access from s to the sea (the sea is denoted by t), and where should the mines be placed? b) Give a mathematical argument that your answer is correct. S 20 a 6 6 2 C 5 4 3 6 10 5 f M 6 e 4 2 2 00 8 h 4 i 6 2. Suppose that we wanted to block access to the sea from inland town s on a river. We can do this by dropping mines in the river, but because the river spreads out in a wide delta with several outlets, the number of mines required depends on where we drop them. The number of mines required in a channel range from a high of 20 to a low of 1 as shown by the network below. In that graph, each channel is shown with a number indicating how many mines will block it. a) What is the smallest number of mines needed to block off access from s to the sea (the sea is denoted by t), and where should the mines be placed? b) Give a mathematical argument that your answer is correct. S 20 a 6 6 2 C 5 4 3 6 10 5 f M 6 e 4 2 2 00 8 h 4 i 6