On the one hand, mathematical software is ubiquitous in mathematics education. On the other hand, word problems are an important part of the curriculum, and they often require modelling skills. This is especially true with optimisation and extrema problems proposed to high school and undergraduate students. We propose two activities around extrema problems, modelling with Dynamic Geometry Software (DGS). The exploration relies on the synchronised representations offered by the DGS. We discuss the different registers of representations used, their synchronisation and the limitations of the models versus the concrete occurrence.