Problem
Ana is a university student with 12 hours available daily, and she wants to distribute her time between study (x) and leisure (y) activities. She wants to maximize her total enjoyment while fulfilling her university obligations. Ana considers leisure to be twice as enjoyable as studying, but she also believes that she should spend at least twice as much time studying as she does on leisure activities. Additionally, she cannot spend more than five hours a day on leisure activities to ensure that she has enough time for her university obligations.
i. Formulate the optimization model for this problem: define the decision variables, objective function, and constraints;
ii. Solve the problem graphically: draw the feasible region, and evaluate its corner points to find the optimal solution;