-3 4 3 (5) -2 3 3 (a) Using the arcs (1,2), (2,3), (4,2), (3,6) and (5,6) find a feasible tree solution (b) Compute the fair prices (dual solution) w; for the FTS of part (a), and she 2.

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Author:Amos Gilat
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1. Consider the following minimum cost network flow problem (here I am following the Chvatal
notation from class, b; < 0 is a supply etc. The numbers next to each arc are the costs for
that arc. Numbers next to each node are supply/demand at that node.)
8
-3
5
4
-6
1/3
3
7
3
3.
6.
3
(a) Using the arcs (1,2), (2,3), (4,2), (3,6) and (5,6) find a feasible tree solution x;ij .
(b) Compute the fair prices (dual solution) w; for the FTS of part (a), and show that the
FTS found there is optimal.
(c) Is the FTS of parts (a,b) unique? Explain why or give a counterexample.
2.
Transcribed Image Text:1. Consider the following minimum cost network flow problem (here I am following the Chvatal notation from class, b; < 0 is a supply etc. The numbers next to each arc are the costs for that arc. Numbers next to each node are supply/demand at that node.) 8 -3 5 4 -6 1/3 3 7 3 3. 6. 3 (a) Using the arcs (1,2), (2,3), (4,2), (3,6) and (5,6) find a feasible tree solution x;ij . (b) Compute the fair prices (dual solution) w; for the FTS of part (a), and show that the FTS found there is optimal. (c) Is the FTS of parts (a,b) unique? Explain why or give a counterexample. 2.
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