<![CDATA[Production scheduling in the multi-product manufacturing industry faces increasingly complex challenges related to the allocation of limited resources such as raw materials, machine hours, and labor. In the era of industry 4.0, operational efficiency is a key determinant of competitiveness, yet many medium-scale industries still rely on intuitive methods that fail to capture the multidimensional trade-offs of production. This study, designed as a simulative case study, aims to apply the linear programming approach using the simplex method to determine the optimal product combination that maximizes profit and to perform a deep sensitivity analysis to evaluate resource resilience within a conceptual manufacturing environment. The simplex algorithm is processed iteratively to reach the optimal solution, followed by sensitivity analysis to identify binding constraint and calculate shadow price. The results indicate that the optimal production composition generated by the simplex model is capable of increasing projected profits 22,4% compared to the conventional heuristic method. Furthermore, sensitivity analysis reveals that machine hours constitute a critical resource (scarce) with a significant positive shadow price, providing a concrete managerial recommendation to prioritize capacity expansion in that sector over labor expansion. It is concluded that the simplex method provides a robust, measurable, and adaptable basis for strategic decision-making in production operations amidst market fluctuations]]>
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