Penentuan Solusi Optimal Pemrograman Kuadratik Menggunakan Metode Beale (Studi Kasus: Produksi Padi Kalimantan Barat)

Authors

  • Rina Robiah Universitas Tanjungpura, Indonesia
  • Mariatul Kiftiah Universitas Tanjungpura, Indonesia
  • Meliana Pasaribu Universitas Tanjungpura, Indonesia

DOI:

https://doi.org/10.15575/kubik.v8i2.29213

Keywords:

basis, concave function, non-basis, partial derivative

Abstract

Rice production in an area is influenced by the area of rice harvesting land. BPS data shows that in 2019-2021 there was a decrease in rice production in West Kalimantan due to a decrease in rice harvest areas. Therefore, optimal utilization of harvested area is needed to obtain maximum average rice production. One method to determine the optimal solution of a quadratic programming problem is the Beale method. In this research, the problem of rice production is formulated into a mathematical model. Furthermore, a quadratic objective function is formed which is a concave function by solving linear equations through a matrix approach. The selected function is solved using the Beale method. The Beale method begins by expressing the base variable into a non-base variable in each iteration process. The optimal solution of the Beale method is obtained when the evaluation value of all partial derivatives of the objective function is less than equal to zero. Based on the research results, the rice harvest area of Mempawah, Sintang, Kapuas Hulu, and Kubu Raya districts were 17,799.53424 ha, 16,364.0143 ha, 6,105.685658 ha, and 32,959.2823 ha, respectively, so that the average maximum rice production was 127.6827216 kw/ha.

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Published

2023-10-03

How to Cite

Robiah, R., Kiftiah, M., & Pasaribu, M. (2023). Penentuan Solusi Optimal Pemrograman Kuadratik Menggunakan Metode Beale (Studi Kasus: Produksi Padi Kalimantan Barat). KUBIK: Jurnal Publikasi Ilmiah Matematika, 8(2), 79–88. https://doi.org/10.15575/kubik.v8i2.29213

Issue

Vol. 8 No. 2 (2023): KUBIK: Jurnal Publikasi Ilmiah Matematika

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