Round Robin volleyball Tournament [closed]

Question

Consider a set of N teams (N even number) that must make a Round Robin Tournament. To each pair i; j, i ≠ j, of teams there is associated level of interest si,j ∈ {1;2;3} of the match between them (1 = minimum interest, 2 = medium interest, 3 = maximum interest). Define a calendar in such a way that:

1. in each day there is at least one game of maximum interest.
2. the minimum average level of interest between all days is maximized.

I have already written the solution for the first constraint, now i want to write the objective function relative to the second point. I have tried to write something like: Maximize the sum of the minimum average for each combination of teams in one matchday but it doesn't work

Answer 1

Assuming binary decision variable $x_{ijd}$ indicates whether teams $i$ and $j$ play each other on day $d$, introduce a decision variable $z$, and maximize $z$ subject to linear constraints $$z \le \frac{1}{N/2} \sum_{i,j} s_{ij} x_{ijd} \quad \text{for all $d$}.$$