Question: Coniser the graph below 8 5 14 10 18 50 6 1 16 11 12 3 9 1. Suppose we have a max flow problem

Coniser the graph below 8 5 14 10 18 50 6 1 16 11

Coniser the graph below 8 5 14 10 18 50 6 1 16 11 12 3 9 1. Suppose we have a max flow problem on the graph, with source node 1 and destination node 6. a. Which of the following are the correct flow balance constraints for nodes 3 and 4? i. X13 = X35 + X34 and X24+X34 = X46 ii. X13 = X35 + X34 and X34 + X14 = X46 iii. X13+ X23 = X34 and X24+X34 = X46 iv. X13 + X34 = X46 and X24 + X34 = X13 b. Which of the following is a correct objective function? Select all that are correct. i. Max X12 + X13 + X 16 ii. Max X16 + X56 + X46 iii. Max X12+X 13+X16+X25+X24+X34+X46+X56 iv. Max X12+X 13+X25+X24+X34+X46+X56 v. Max X12+X15+X56 vi. Max X13+X34+X46 c. Given that the value of the max flow is 71, what is the value of the minimum cut on this graph? i. 78 ii. 71 iii. 80 iv. 70 v. 75 d. How many cut arcs are in the minimum cut? i. 1 ii. 2 iii. 3 iv. 4 v. 5

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