Analysis of Solutions of Linear System Using the Gaussian Elimination Method for Production Optimization in the Bakery Industry
Abstract
The bakery industry faces challenges in optimizing production due to limited raw materials and multiple product types. This study aims to analyze a system of linear equations representing the relationship between product quantities and raw material usage using the Gaussian elimination method. A case study involving bread, sweet bread, and cake production was conducted based on the availability of flour, sugar, and eggs. The system was formulated and solved using Gaussian elimination to obtain its general solution. The results show that the system has infinitely many solutions, indicating multiple feasible production combinations that fully utilize available resources. One practical solution identified is the production of 20 units of bread, 30 units of sweet bread, and 20 units of cake. This combination ensures optimal use of raw materials without waste. The findings demonstrate that Gaussian elimination is an effective method for supporting production planning and decision-making. Overall, linear algebra provides a reliable approach for optimizing resource allocation in the bakery industry.
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DOI: https://doi.org/10.31004/jele.v11i2.2348
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