Question: An integer program to maximize the total rating for both teams combined. There are two teams and a pool of 8 players. The ratings for

An integer program to maximize the total rating for both teams combined. There are two teams and a pool of 8 players. The ratings for each player by the Coach of each team is:

Team/Player 1 2 3 4 5 6 7 8
1 7.2 8.1 9 8 7.5 9.2 8.5 9.3
2 9.3 8.5 9.2 7.5 8 9 8.1 7.2

Each Team has to have exactly 5 players. Two players will have to play on both teams.

I know maximize z = 7.2X11+8.1X12+9X13+8X14+...+7.2X28. One of the other constraints is X11+...+X18=5. The constraints I am having issue with is the two players will have to play on both teams.

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