Formulate an integer programming model for this problem. Your objective function should maximize the total happiness level of all students based on given constraints. Clearly define your objective function, parameters and variables.

The following constraints must be considered:

E$1$ and E$4$ are siblings and cannot receive the same superhero figures $($For instance, If Superman and Hulk are given to E$1$ then any of these two characters cannot be given to E$4).$

E$3$ and E$9$ will fight if they receive different superhero figures. Therefore, E$3$ and E$9$ each have to take at least one of the same kind of superhero figure.

If Superman and Flash are assigned to the same student, the happiness level will decrease by $20\%$ because the student finds these characters too similar.

E$2,$ E$5$ and E$11$ are in competition and must not receive the same superhero figures.

If a student receives their two most preferred figures, their happiness level will increase by $30\%.$

If a student receives their two least preferred figures, their happiness level will decrease by $50\%.$