Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and learning in higher education. Method: By using an observational methodology, we present the representation patterns used by three students in their fifth year of an undergraduate mathematics degree at the University of Granada (Spain). The patterns were obtained through protocol analysis in which students' written production was complemented with their spoken thinking protocols. The instrument used was prepared intentionally for this study and was composed of three optimization problems. Students solved the instrument individually in an isolated environment while being video-recorded. Results: We designed a framework for protocol analysis and used it to analyze the transcriptions of students' productions. Results are presented in the form of a microscopic analysis of the particular cases, with detailed records of the representations used by the students, translation between records and the time used in these actions. These elements are then used to define a profile of each Problem Solver, which was found to be different for the three cases. Discussion and conclusions: The framework designed for the microscopic analysis of problem solving protocols was useful for describing the representations and the translations between them during the problem-solving process. The segmentation and coding process made evident the need to include episodes which initially were not identified as representations. A characterization of the Problem Solvers shows a strong connection between students' success in solving optimization problems and their skill in using representations. (Contains 3 figures, 2 tables, and 3 footnotes.)