<![CDATA[In mathematics education, problem-solving is a core element that involves stages for analyzing the problem, planning a solution, applying strategies, and reviewing the results. In the Industrial Engineering Study Program, the ability to problem-solve in optimization mathematics plays a crucial role. This ability can be used as a foundation for minimizing costs, designing production processes, and more. The aim of this research is to determine students' problem-solving abilities in solving problems related to multivariable optimization mathematics analytically without constraints. This study is a descriptive qualitative research and was conducted with six students as research subjects. The instruments used include test questions and interview guidelines. The results show that subjects with low problem-solving abilities tend to only perform two problem-solving stages: understanding the problem and planning the solution. However, they do not execute the plan smoothly and fail to review it. Subjects in the moderate category perform three problem-solving stages, including understanding the problem, choosing a solution strategy, and implementing the plan. Subjects in this category often lack precision in calculations and miss the step of reviewing their answers. Subjects with high problem-solving abilities effectively perform all four problem-solving stages: understanding the problem, creating a solution plan, executing the plan, and reviewing the steps until the final result. Keyword: Problem-Solving, Optimization Mathematics, Multivariable Function, Analytically]]>
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