7. (10 points) In the following figure, if the numbers next to each link in the figure denote the flow capacities. The maximum flow problem to find maximum flow from node 1 to node 6 can be formulated by a linear program as follows: max z=xo X12-X23 + X24 x24-x43 +x46 s.t. x X12 x13 + %24 35 X35- X56 X12 S 6 x13 S 2 x23 3 1 x24 S 3 335 S 7 x43 S 3 X46 3 2 X12, X13, X23-X24, X35, X43, X46, X56 0 where the decision variable xiy denotes the flow on the link (i,j) and the decision variable xo indicates the maximum flow that can be sent from node 1 to node 6. Using the duality table of page 1 to find the dual problem of this one. (Hint: for first 6 constraints, please move the right-hand-side decision variables to left-hand- side before performing the duality). SIE340 Final Exam- Summer I 2017 Page 10 of 12
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