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All Journal MATHunesa: Jurnal Ilmiah Matematika JUMAT: Jurnal Matematika
Mey Gracia Sitanggang
Universitas Negeri Medan
Education Mathematics

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PENERAPAN ALGORITMA EUCLID PADA PENYELESAIAN PERSAMAAN DIOPHANTINE LINEAR Mey Gracia Sitanggang; Aldha Aulia Imtiyaz Hasibuan; Gisa Sahwani; Hery Judika Lumban Tobing; Istiqfasha Purwadi; Winda elyca Pasaribu
MATHunesa: Jurnal Ilmiah Matematika Vol. 14 No. 01 (2026)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/mathunesa.v14n1.p184 - 193

Abstract

Penelitian ini membahas penerapan Algoritma Euclid dalam menyelesaikan persamaan Diophantine linear, yaitupersamaan polinomial dengan dua atau lebih variabel yang solusi yang dicari adalah bilangan bulat. PersamaanDiophantine linear umumnya berbentuk ax + by = cax + by = cax + by = c, dengan a, b, dan c menjadi bilanganbulat. Penelitian ini menggunakan metode deskriptif-eksploratif, dengan pendekatan studi literatur dan analisisalgoritma. Fokus utama adalah bagaimana Algoritma Euclid digunakan untuk mencari faktor persekutuan terbesar (FPB) dari dua atau lebih koefisien, yang menjadi syarat utama agar suatu persamaan linier memiliki solusi bilangan bulat. Dalam penelitian ini ditunjukkan bahwa persamaan memiliki solusi hanya jika FPB dari koefisien pembagian konstanta pada ruas kanan persamaan. Penelitian ini juga memberikan beberapa contoh soal persamaan linear dua, tiga, dan empat variabel, beserta langkah-langkah penyelesaiannya menggunakan Algoritma Euclid. Hasil yang diperoleh menunjukkan bahwa algoritma ini tidak hanya efisien dan sistematis, tetapi juga memberikan solusi umum dan spesifik yang dapat berfungsi. Pemahaman terhadap konsep dasar teori bilangan, khususnya FPB, sangat penting untuk menerapkan algoritma ini secara efektif dalam menyelesaikan masalah-masalah persamaan Diophantine linear.
Struktur Graf Berarah pada Sistem Kekerabatan Batak Toba (Dalihan Na Tolu) Mey Gracia Sitanggang; Rawiyah; Goffri Simarsoit; Ian Pedrosa manatap Lumban Gaol; Hery Judika Lumban Tobing; Tomi Arianto
JUMAT: Jurnal Matematika Vol. 3 No. 2 (2025): JUMAT, Desember 2025
Publisher : Institut Agama Islam Negeri Fattahul Muluk Papua

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Abstract

This study aims to examine the structure of the Batak Toba kinship system (Dalihan Na Tolu) using a directed graph theory approach. The Dalihan Na Tolu system is a social philosophy of the Batak Toba community consisting of three main elements, namely hula-hula, boru, and dongan sabutuha, which are interconnected within customary and marital structures. This research employed a qualitative descriptive method with a mathematical modeling approach. Data were collected through interviews, observations, and the study of tarombo documents of Raja Nai Pospos’ descendants, particularly the lineage of Toga Marbun and Lumban Gaol. The data were then represented in the form of tree graphs and directed graphs. The results showed that the Batak Toba kinship system is patrilineal, allowing it to be modeled as a tree graph without cycles in the lineage structure. Meanwhile, customary and marital relations among clans form asymmetric directed graphs because the relationships between vertices have different directions and social meanings. In addition, cycles among clans were identified, representing the concept of mambolahi in Batak Toba customs. The analysis of adjacency matrices, in-degree, and out-degree indicated that several clans have higher levels of social connectivity than others. Therefore, directed graph theory is capable of representing the social structure of Dalihan Na Tolu systematically, visually, and mathematically, while also contributing to the development of social mathematics and ethnomathematics studies based on local culture.
Optimasi Keputusan Produksi untuk Meningkatkan Keuntungan Usaha Minuman Kafe melalui Pendekatan Program Linier Nerli Khairani; Rawiyah; Mey Gracia Sitanggang; Ian Pedrosa manatap Lumban Gaol
JUMAT: Jurnal Matematika Vol. 3 No. 2 (2025): JUMAT, Desember 2025
Publisher : Institut Agama Islam Negeri Fattahul Muluk Papua

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Abstract

The coffee shop business is one of the Micro, Small, and Medium Enterprises (MSMEs) sectors that is experiencing rapid growth, but often faces obstacles in optimizing profits due to limited production resources. This study aims to determine the optimal production combination that can maximize the profits of a cafe beverage business through a linear programming approach. This research is a quantitative study with a descriptive-optimization approach conducted at one of the cafe beverage businesses in the period April–May 2026. The research subjects consisted of two decision variables, namely coffee drinks (X₁) and non-coffee drinks (X₂), with five production resource constraints. Data were collected through observation, interviews, and documentation using observation sheets, interview guidelines, and production and sales data. Data analysis was carried out using graphical methods in linear programming to determine the feasible region and optimal solution, and validated using POM-QM software for Windows. The results showed that the optimal solution was obtained at point (40,20), namely 40 units of coffee drinks and 20 units of non-coffee drinks, with a maximum profit of IDR 280,000. In conclusion, the combined production of both products is more optimal than a single product because it maximizes the use of limited resources. The linear programming approach has proven effective as a basis for more rational, efficient, and data-driven production decisions.
Co-Authors Aldha Aulia Imtiyaz Hasibuan Arianto, Tomi Gisa Sahwani Goffri Simarsoit Hery Judika Lumban Tobing Hery Judika Lumban Tobing Ian Pedrosa Manatap Lumban Gaol Istiqfasha Purwadi Nerli Khairani Rawiyah Winda elyca Pasaribu