Mahmudah, Ulfatu (2019) Analisis persyaratan KUHN tucker pada masalah optimasi hasil pertanian. Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.
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Abstract
INDONESIA:
Pertanian merupakan kegiatan yang memiliki peran strategis dalam perekonomian nasional. Hal ini digambarkan melalui kontribusi nyata seperti; penyediaan bahan pangan, bahan baku industri, sumber pendapatan serta pelestarian lingkungan. Tujuan dari penelitian ini adalah membentuk model matematika untuk mengoptimalkan hasil pertanian di kabupaten Cilacap serta menyelesaikan model dengan menggunakan persyaratan Kuhn Tucker.
Model matematika dalam penelitian ini merupakan model nonlinier yang dibentuk menggunakan metode kuadrat terkecil, fungsi tujuan dari model tersebut adalah memaksimalkan hasil pertanian di kabupaten Cilacap yang mana dipilih dua jenis tanaman yaitu padi ladang dan padi sawah. Permasalahan pemrograman nonlinier diselesaikan menggunakan persyaratan Kuhn Tucker. Syarat yang harus dipenuhi untuk optimum adalah turunan parsial pertama dari fungsi tujuan terhadap semua variabel dan pengali Lagrange bernilai nol.
Berdasarkan perhitungan, diperoleh fungsi tujuan S(x,y)=-3,23594y^2+1,491518x+3,841733y-0,071623242 dengan fungsi kendala x≤139,451, y≤11,265dan x,y≥0 yang mana setelah dilakukan perhitungan menggunakan persyaratan Kuhn Tucker didapatkan hasil optimal untuk rata-rata produksi tanaman padi ladang dan padi sawah yaitu 3,4447688569 kwintal dengan luas panen padi sawah 1,411 hektar dan luas panen padi ladang 0,5936 hektar.
ENGLISH:
Agriculture is an activity that has a strategic role in the national economy. This is illustrated by tangible contributions such; supply of food, industrial raw materials, sources of income and environmental preservation. The purpose of this study are farming a mathematical model to optimize agricultural products in Cilacap district and to solve the model by using the Kuhn Tucker conditions.
The mathematical model in this study is a nonlinear model that was formed using the least squares method, the objective function of the model is to maximize agricultural yields in Cilacap district which two types of plants are chosen, namely rice and rice lowland. Nonlinear programming problems are solved using Kuhn Tucker's requirements. The conditions that must be met for the optimum are the first partial derivative of the objective function of all variabels and Lagrage multipliers are zero.
Based on the calculation, the objective function is obtained n S(x,y)=-3,23594y^2+1,491518x+3,841733y-0,071623242 with constraint functions x≤139,451, y≤11,265 and x,y≥0 which after calculation using the Kuhn Tucker method is obtained the optimal yield for the average production of rice and rice lowland is 3,4447688569 quintals with harvested rice fields of 1,411 hectares and rice lowland harvested area of 0,5936 hectares.
Item Type: | Thesis (Undergraduate) | |||||||||
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Supervisor: | Kusumastuti, Ari and Abdussakir, Abdussakir | |||||||||
Contributors: |
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Keywords: | hasil pertanian; optimasi; metode kuhn tucker; agricultural products; optimization; kuhn tucker's conditions | |||||||||
Departement: | Fakultas Sains dan Teknologi > Jurusan Matematika | |||||||||
Depositing User: | Heni Kurnia Ningsih | |||||||||
Date Deposited: | 24 Apr 2020 10:21 | |||||||||
Last Modified: | 24 Apr 2020 10:21 | |||||||||
URI: | http://etheses.uin-malang.ac.id/id/eprint/15173 |
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