This paper presents an exploratory analysis on the convenience and feasibility of using free software or commercial software as a support tool in the teaching of subjects in engineering programs develop competence in mathematical modeling. In particular, this work presents elements to encourage discussion about the choice of commercial or free solvers for teaching linear mixed models and their solution, as initiation phase to the field of mathematical modeling. The experimental stage used the linear instances provided by the NETLIB library and its quality outcome was compared through the CPU time and the ability to provide solution to the instances in order to evaluate it as a strong criterion that will support the choice of commercial solvers instead of the open source counterparts. Two open source solvers and three well known commercial solvers were tested finding out there is no significant difference between the performances reported by the commercial application and one of the open source counterpart. As a result, the use of open source solvers should be considered as a real alternative in the teaching and solving process in the academic context.