7. (10 points) Consider a local baseball league with four teams 70, 71, 72, 73. You...

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7. (10 points) Consider a local baseball league with four teams 70, 71, 72, 73. You are rooting for the team zo and, at some time during the season, you are wondering if ro can still win the championship. Each pair of teams play 10 games during the season. The table below shows the results so far; the entry in row x, and column r, is the number of times the team z, has defeated the team , so far (there are no draws). Хо II X2 I3 6 4 3 3 8 7 21 3 5 2 5 1 2 To x1 X2 Is If zo wins all its remaining games, how many wins will it have altogether? X2 De Is Y12 • How many more times will r, play z,, for 1 ≤ i ≤j≤ 3? 913 Y/23 Assuming zo does win all its remaining games, how many more games can each of #1, #2 and r3 win so that zo is the champion (has more wins than every other team)? Create a model for this problem by assigning capacities to the above network. What should the value of max flow be so that o has a chance to be the champion? Find the minimum cut for the model network you have created. What conclusion can you make from value of the min cut? 7. (10 points) Consider a local baseball league with four teams 70, 71, 72, 73. You are rooting for the team zo and, at some time during the season, you are wondering if ro can still win the championship. Each pair of teams play 10 games during the season. The table below shows the results so far; the entry in row x, and column r, is the number of times the team z, has defeated the team , so far (there are no draws). Хо II X2 I3 6 4 3 3 8 7 21 3 5 2 5 1 2 To x1 X2 Is If zo wins all its remaining games, how many wins will it have altogether? X2 De Is Y12 • How many more times will r, play z,, for 1 ≤ i ≤j≤ 3? 913 Y/23 Assuming zo does win all its remaining games, how many more games can each of #1, #2 and r3 win so that zo is the champion (has more wins than every other team)? Create a model for this problem by assigning capacities to the above network. What should the value of max flow be so that o has a chance to be the champion? Find the minimum cut for the model network you have created. What conclusion can you make from value of the min cut?

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Answer and Explanation 1 If x0 triumphs in every game left it will have a total of 8 6 10 10 34 vict... View the full answer