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All Journal JUMAT: Jurnal Matematika Jejak digital: Jurnal Ilmiah Multidisiplin
Ian Pedrosa Manatap Lumban Gaol
Universitas Negeri Medan
Economics, Econometrics & Finance Education Languange, Linguistic, Communication & Media Mathematics Social Sciences Other

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Implementasi Integral Garis pada Medan Vektor dalam Perhitungan Usaha Gaya Alpha Reynaldi Pernanda Tanjung; Desta Asina Nainggolan; Dewi Efarina Simanjuntak; Ian Pedrosa Manatap Lumban Gaol; Rawiyah Rawiyah; Alvi Sahrin Nasution; Hamidah Nasution
Jejak digital: Jurnal Ilmiah Multidisiplin Vol. 2 No. 3 (2026): MEI 2026
Publisher : INDO PUBLISHING

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.63822/rym5yy09

Abstract

Line integrals are one of the fundamental concepts in advanced calculus used to determine the accumulation of a quantity along a specific path within a vector field. This concept has various applications in science, particularly in physics and engineering, especially in calculating the work done by a force acting on an object moving along a certain trajectory. This study aims to examine the application of line integrals in vector fields for calculating the work of a force and to analyze the relationship between a particle’s path and the resulting work. The research method employed is a qualitative approach with mathematical analytical study through theoretical review and calculation of line integrals in two-dimensional vector fields. The analysis process involves defining the vector field function representing the force, parameterizing the particle’s path, and evaluating the line integral to obtain the resulting work. The results show that the work done by a force can be determined through the evaluation of a line integral along the path taken by the particle. Furthermore, the analysis of the vector field indicates that the field is conservative, meaning that the work depends only on the initial and final points of the displacement, not on the shape of the path taken. The visualization of the vector field, particle trajectory graphs, and calculation tables helps provide a clearer understanding of the application of line integrals in analyzing work. Therefore, the concept of line integrals in vector fields can be used as an effective mathematical approach to explain the relationship between force and displacement in a physical system.  
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 Alpha Reynaldi Pernanda Tanjung Alvi Sahrin Nasution Arianto, Tomi Desta Asina Nainggolan Dewi Efarina Simanjuntak Goffri Simarsoit Hamidah Nasution Hery Judika Lumban Tobing Mey Gracia Sitanggang Nerli Khairani Rawiyah Rawiyah Rawiyah