Optimization (linear, integer, binary or mixed programming)

Problem:

The blue magic team, after "regular" seasons, urgently requires the Copa Libertadores to qualify for the group stage. You, as a diehard fan, put yourself at the disposal of the new management and they decide to give you a whole programming model, remembering that the Chilean championship has 17 teams, that they play all against all, and that the first two qualify for the group stage. In addition, as in any championship, the winner gets 3 points, the draw 1 and the loss zero.

1) Model the problem in such a way that it maximizes the amount of points, with which the magic team does NOT reach the Copa Libertadores.

2) Imagine that on the first date, the magical blue team faces its classic rival, Cruzalbo, where with a goal by Marcelo Puntete's Chilean, it gets its first three points. What can this information add to the model?

3) What advice would you give to the new management for the magic team to qualify?

To model a problem you must have: Decision variables, objective function, and constraints. Also, remember that you cannot multiply binary variables with integer variables.