Open Problem $(50\%)$ The Royal Spanish Tennis Federation $($RFTE$)$ must decide which tennis players

will represent the country at the $2024$ Paris Olympics in the categories of: singles$,$ men's doubles,

women's doubles, and mixed doubles. This is the information available about the possible choices:

The following conditions must be considered when making the selection:

The RFTE can only take a total of six athletes. Three from each gender.

Each player must compete in two categories: singles and one of the doubles.

If Rafael Nadal is chosen, he must obligatorily play men's doubles with Carlos Alcaraz.

Since they are a pair in the WTA circuit, Cristina Bucsa and Sara Sorribes will participate in

women's doubles.

Due to past issues, Bucsa and Granollers cannot pair up in mixed doubles.

The RFTE's goal is to minimize the average ranking of the selected players. To calculate this

objective, consider the following example: if singles are played by Alcaraz, Nadal, and Mart$$nez$,$

the average will be $\frac{2+9+42}{3},$ and if men's doubles are Nadal and Alcaraz, the average for doubles

will be $\frac{95+84}{2},$ and if mixed doubles are Mart$$nez and Badosa, the average will again be $\frac{65+55}{2}.$

Grading Breakdown:

$5\%$ Define the elements of the model and notation: definition of sets, parameters, decision

variables, and their respective mathematical notation.

$5\%$ Verbalize the structure of the model: description in words of the model structure with

decisions, objective function, and constraints.

$25\%$ Formulate the model concretely and abstractly$.$