Journal of Basic and Applied Research International

Aims: This study aims to analyse students’ performance in mathematical modelling and identify error patterns when solving a linear programming problem using the simplex method.

Study Design: A descriptive–exploratory study was conducted.

Place and Duration of Study: The study was conducted in a mathematics education program at a public university in Indonesia during a semester in which students studied linear programming.

Methodology: Twenty-four undergraduate students completed a contextual optimisation task requiring model construction and solution using the simplex method. Students’ responses were analysed using a mathematical modelling framework and Newman’s error analysis. Descriptive and cross-case analyses were conducted to identify performance trends and dominant error types.

Results: Students demonstrated strong performance in early modelling stages, including understanding the problem (M = 2.88), simplifying/structuring (M = 2.88), and mathematising (M = 2.75). However, performance declined substantially in the working mathematically stage (M = 1.29) and remained low in interpreting (M = 0.38) and validating (M = 0.33). The most frequent errors were process skill errors, particularly those related to elementary row operations during simplex iterations (P4), which appeared in the majority of student responses. Cross-pattern analysis revealed that low performance in algorithmic stages was consistently associated with procedural errors, while difficulties in interpreting and validating were linked to failure in recognising optimality conditions.

Conclusion: The findings indicate a gap between students’ modelling competence and procedural fluency in executing the simplex method. Strengthening algorithmic reasoning alongside modelling instruction is essential to support students’ complete engagement in optimisation tasks.