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All Journal Journal of Mathematics Instruction, Social Research and Opinion Perspectives in Mathematics and Applications (PERMATA)
Bayu Sukmaangara
Universitas Islam Negeri Siber Syekh Nurjati Cirebon
Humanities Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Engineering Languange, Linguistic, Communication & Media Mathematics Physics Social Sciences

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Application of the Derivative Concept to Determine the Maximum Profit Point of Nasi Lengko Traders in Cirebon Bayu Sukmaangara; Devan Fariliyanto; Fika Triramadani; Farisha Dwi Anggia
Journal of Mathematics Instruction, Social Research and Opinion Vol. 5 No. 1 (2026): March
Publisher : MASI Mandiri Edukasi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58421/misro.v5i1.912

Abstract

This study employs the concept of differentials, or mathematical derivatives, to determine the maximum profit points for Cirebon-style Nasi Lengko UMKM, namely Trader A and Trader B, both located in Sunyaragi Village. The study employs a quantitative descriptive approach, using interview data on capital, selling price, revenue, and production quantity. The data are then formulated as functions of total cost, revenue, and profit, using the first derivative to identify the critical points and the feasible domain. The results show that Trader A, with a capital of Rp 101,000 and a capacity of 20 portions, obtains a maximum profit of Rp 99,000 when all production is allocated to egg Nasi Lengko priced at Rp 10,000 per portion, due to a constant negative derivative. Meanwhile, Trader B, with a capital of Rp 200,000 and a capacity of 40 portions, achieves a maximum profit of Rp 200,000 by producing Nasi Lengko at a price of Rp 10,000 per portion, with a constant positive derivative. This study demonstrates that the concept of derivatives can help optimise production decisions in traditional food UMKM, despite limitations such as a small sample size and limited variable-cost data. Further studies are recommended to use a wider sample and more comprehensive data.
Peta Penelitian SEIRS-Vaksin COVID-19: Analisis Tren, Temuan, dan Tantangan Model Matematika Muhamad Fahri Fauzan; Alya Ramadhani; Dara Maywanti; Aban Subanul Fahmi; Bayu Sukmaangara
Perspectives in Mathematics and Applications Vol 1 No 02 (2025): Desember
Publisher : Kreasi Pustaka Mandiri (Krestama)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.66256/permata.v1i2.25

Abstract

The control of the COVID-19 pandemic requires mathematical models that are able to accommodate complex immune dynamics, especially waning immunity phenomena and vaccination interventions. This study conducted a Systematic Literature Review using the PRISMA protocol to map trends, findings, and methodological challenges in SEIRS-Vaccination modeling. Of the 80 articles identified in the initial stage, 56 articles met the inclusion criteria and were analyzed. Furthermore, 11 articles were selected through purposive sampling techniques as representative samples for in-depth comparative analysis of five main methodology categories: Deterministic (ODE), Optimal Control, Fractional Order, Data Assimilation/Stochastic, and Spatial. The results of the literature synthesis reveal a significant paradigm shift from classical deterministic models that focused on stability analysis  static towards a more adaptive model. Specifically, this study identifies the use of the Ensemble Kalman Filter for estimation of dynamic parameters and Optimal Control Theory for resource allocation strategies as the dominant methodological trends. The model's findings consistently validate that vaccination rate is the most sensitive intervention parameter, but its long-term effectiveness is highly dependent on the duration of immunity. The study concludes the need to develop a hybrid model that integrates stochastic approaches and optimal control to generate more precise policy recommendations in the future.
Co-Authors Aban Subanul Fahmi Alya Ramadhani Dara Maywanti Devan Fariliyanto Farisha Dwi Anggia Fika Triramadani Muhamad Fahri Fauzan