The goal of this exercise is to fill a square area \([0,250]\times[0,100]\) with 25 circles. The model can choose the \(x\) and \(y\) coordinates of the center of each circle and the radius. So we have as variables \(\color{darkred}x_i\), \(\color{darkred}y_i\), and \(\color{darkred}r_i\). The circles placed inside the area should not overlap. The objective is to maximize the total area covered.

A solution is: