Question $2$

$(15$ points$)$ A data scientist is engaged in training two machine learning models: Model A and Model B$.$ Each model demands specific computational resources and data processing time. Model A needs $3$ hours of computational resources and $5GB$ of data. Model B requires $4$ hours of computational resources and $2$ GB of data. The data scientist has a total of $24$ hours of computational resources and $20GB$ of data at their disposal. The goal is to maximize the models' performance score, with Model A contributing $80$ points and Model $B$ contributing $70$ points each time.

Develop a linear programming model to find the optimal quantity of each model to train in order to achieve the highest total performance score.

Note: Clearly define all sets, parameters, and decision variables in your model.