Question: 4. Find the maximal flow from node 1 to node 7 in the following network. 3 2 5 a 3 3 2 3 4 3

4. Find the maximal flow from node 1 to node 7 in the following network. 3 2 5 a 3 3 2 3 4 3 1 1 3 3 5 6 6 Decision variables: xy = amount of flow from node i to nodej Objective function: Maximize the flow through the network: Maxx? Please fill the constraints for the problem. Constraints: (1) x12 + x1 + ---X70 (node 1) (2) X4+x23 - -- X2 X320 (node 2) (3) X34 + X36-X- =0 (node 3) X42+ x4 + X45+ + X47 - 14 -- ** - *4- X54 - 4 - 0 (node 4) (5) XS2 + x4 + -- XS - X4 - 0 (node 5) (6) .X64X67- -X460 (node 6) X91-X47 - X's - X 0 (node 7) Capacity for each are: (8) 1234 (14) 365 (20) X5253 (9) Xu 3 (15) 53 (21) X5454 (10) 1454 (16) 14 = 5 (22) X5 S2 (11) X452 (17) Xas 53 (23) X51 (12) X2 53 (18) X4651 (24) K67 55 (13) X3 (19) XS 3 (7)

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