$($i$)$ The Higher Education Authority in a state budgeted $1,500,00,000$ for the bonuses and merits of $503$ university teachers. A Salary Differential Evaluation Board, comprising Campus Social Board members, administrators, supervisors, and teachers, determined the three variables that should affect bonuses and merits. If we name these variables as CM$1,$ CM$2$ and CM$3,$ we obtain:

CM$1$: Teachers' performance measured by the university evaluation instrument. CM$2$: General services to the university and its students, including voluntary activities, etc.

CM$3$: Professional development, measured by a formula, which includes teaching merits, research, participation in management tasks, etc.

All three variables above are measured on a scale ranging from $1($low$)$ to $5($high$).$ The points scored during $1$ year determine bonuses and merits for the following year. In $2022,$ the sum of the points of these variables was:

$CM1=1,625$

$CM2=1,409$

$CM3=1,387$

The Evaluation Board recommended, and the Campus Social Board accepted, the following rules: