[b]Pemrograman Linear [/b]merupakan metode matematik dalam mengalokasikan sumber daya yang langka untuk mencapai suatu tujuan seperti memaksimumkan keuntungan dan meminimumkan biaya. Sumber daya yang langka tersebut merupakan kendala, yang berupa fungsi linear, sedangkan tujuan merupakan fungsi tujuan yang berupa fungsi linear juga. PL diterapkan dalam masalah bisnis, ekonomi, industri, militer, sosial, teknik, dan lain-lain.[br][br]Penyelesaian PL dengan metode grafik dapat dilakukan dengan 3 cara, yaitu :[br][br][b]Metode Garis Selidik[/b][br]Metode garis selidik dilakukan dengan cara menggeser garis selidik secara sejajar ke arah kiri, kanan, atas, atau bawah sampai garis tersebut memotong titik-titik pojok daerah himpunan penyelesaian sistem pertidaksamaan linear dua variabel.[br][br]Bentuk umum fungsi tujuan dinotasikan dengan [img width=138,height=18]data:image/png;base64,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[/img][br][br]Bentuk umum garis selidik dinotasikan dengan [img width=78,height=18]data:image/png;base64,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[/img] dgn [img width=37,height=18]data:image/png;base64,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[/img]. Dimana [img width=9,height=18]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAXCAMAAADqZkX0AAAAAXNSR0IArs4c6QAAAFdQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOpDbZgAAZjo6ZmaQZrbbZrb/kDoAkDo6kNv/tmYAttv/tv//25A627Zm29u22////7Zm/9uQ/9u2//+2///bS3pOugAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAZUlEQVQoU5WPyRKAIAxDW5XNBcENEP7/O60wcPNgT5k0r5kC/B6L/d4gy1zVSctmR7U07TsDJ2I2DooHMeed5ZDWEotK3qMpRBCI9SihL13izAVRGpImVPNrom5CAbwYtt9/fAIPIYQD8gYAC60AAAAASUVORK5CYII=[/img] sembarang bilangan yang dipilih.[br][br]Langkah-langkah penyelesaian dengan metode garis selidik:[br]1. Membuat model matematika[br]2. Menentukan daerah himpunan penyelesaian[br]3. Menentukan persamaan garis selidik dan fungsi tujuannya[br]4. Mencari nilai minimum atau maksimum[br]  [br]Nilai maksimum didapatkan dengan menggeser garis selidik secara sejajar ke arah kanan atau atas sampai memotong titik paling jauh dari daerah himpunan penyelesaian.[br][br]Nilai minimum didapatkan dengan menggeser garis selidik secara sejajar ke arah kiri atau bawah sampai memotong titik paling dekat dari daerah himpunan penyelesaian.[br][br][b]Metode Titik-Titik Sudut[/b][br]Metode titik sudut dilakukan dengan cara menentukan nilai optimum dari fungsi tujuan yang dicapai (dipenuhi) oleh salah satu titik sudut dari daerah himpunan penyelesaian.[br][br]Langkah-langkah penyelesaian dengan metode titik-titik sudut :[br]1. Menentukan daerah layak[br]2. Menentukan koordinat titik-titik sudut daerah layak [br]3. Menentukan nilai fungsi dari semua titik sudut [br]4. Menentukan nilai fungsi yang optimal[br][br][b]Metode Gradien[br][/b]Metode gradien adalah suatu metode yang secara langsung menggunakan gradien. Dengan metodegradien, akan langsung dapat kita tentukan titik pojok yang menyebabkan suatu fungsi tujuan memiliki nilai optimum (maksimum atau minimum).[br][br]Langkah penyelesaian menggunakan metode gradien :[br]1. Menentukan gradien garis dari semua kendala dan fungsi tujuan dengan [img width=52,height=25]data:image/png;base64,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[/img] [br] untuk fungsi [img width=77,height=18]data:image/png;base64,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[/img][br]2. Mengurutkan nilai gradien dari kecil ke besar [br]3. Menentukan posisi nilai gradien fungsi tujuan, misalkan terletak di antara nilai gradien kendala ke-i dan  ke-j [br]4. Menentukan titik optimal yang merupakan perpotongan garis dari kendala ke-i dan garis dari kendala ke-j[br][br]Misalkan ada fungsi tujuan [img width=138,height=18]data:image/png;base64,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[/img] dengan gradien [img width=18,height=20]data:image/png;base64,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[/img], dan terdapat dua kendala yaitu kendala I dengan gradien [img width=18,height=18]data:image/png;base64,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[/img] dan kendala II dengan gradien [img width=19,height=18]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAXCAMAAAAm/38fAAAAAXNSR0IArs4c6QAAAGNQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OmaQOma2OpDbZgAAZgA6ZjoAZrbbZrb/kDoAkGZmkJBmkLbbkNv/tmYAtmY6tv//25A625Bm27Zm29u22////7Zm/9uQ//+2///bkLNwxgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAl0lEQVQoU91S2RLCIAxMWqxHVVChIpbj/7+yIYwOeIzv7lPY3WSTGQD+BGlCMbuhk1R0ujrqpn1/PiYlTjqOu+Zai/Q2KOFVMP0VkloBhEHWHUlRA3OeHBUKl3ONmAHuB8Qty8zZx7i4v4Ar22WOzZQd2BvWWeDYss+EG5pF1nbrZ6wrEW+wX3hPvG/uKa1xRMIH4ffXWACQMQfxv4RDkgAAAABJRU5ErkJggg==[/img], maka akan ada tiga kemungkinan yang terjadi, yaitu :[br]1. [img width=94,height=20]data:image/png;base64,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[/img] artinya nilai optimum diperoleh pada titik pojok garis pertama.[br]2. [img width=94,height=20]data:image/png;base64,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[/img] artinya nilai optimum diperoleh pada perpotongan kedua garis.[br]3. [img width=94,height=20]data:image/png;base64,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[/img] artinya nilai optimum diperoleh pada titik pojok garis kedua.[br][br]Syarat metode gradien :[br]1. Semua gradien fungsi tujuan dan kendalanya harus negatif[br]2. Tanda ketaksamaannya harus sama semua ([img width=11,height=18]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAAXCAMAAAAMT46wAAAAAXNSR0IArs4c6QAAAEJQTFRFAAAAAAAAAAA6ADo6ADpmOgAAOmaQZjo6ZpC2ZrbbkGY6kLbbkNv/tmYAtpBmttv/27aQ29u22////9u2/9vb///b+QISCgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAARklEQVQoU2NgoD0QFWDngdsiyM7Ixg/lCXOxsnBD2SJ8rMwcQnBlvEycyA5DkwVKIeuFqEQ2GSyAYi/CZEYYYEK4ivqBAABhiwHzmgMWuQAAAABJRU5ErkJggg==[/img] semua atau [img width=11,height=18]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAAXCAMAAAAMT46wAAAAAXNSR0IArs4c6QAAAFFQTFRFAAAAAAAAAAA6ADo6ADpmOgAAOjoAOjpmOmaQZjoAZjo6ZpC2ZrbbkGY6kLbbkNv/tmYAtmY6tpBmttv/27Zm27aQ29u229v/2////9vb///bRravFAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAATElEQVQoU2NgoB0Q5BBGNlxKlJOJWxxZRFKIlZlHAllEjJeRnQ9FEy8TP5wvxoWQlRRkZeGD6pUSYWPiRpiDZi+aBwUYYQDJZOoHAgDUUQKPFMfBiwAAAABJRU5ErkJggg==[/img] semua)[br]3. Banyaknya kendala bisa lebih dari 2[br]4. Dibatasi oleh sumbu [img width=8,height=18]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAXCAMAAAAFpC7KAAAAAXNSR0IArs4c6QAAAFFQTFRFAAAAAAAAAAA6AABmADpmADqQOgAAOma2OpDbZgAAZmaQZrb/kDoAkDpmkGY6kLaQkNv/tmY6tv//25A625Bm27Zm2////7Zm/9uQ//+2///bg/OZ8AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAUElEQVQYV2NgoBWQ4mPkYGAQZBJgYBAREGYWEuGG2CTOxM8OtVOSk0UIypTiASqGKmBjFYOwJLlEmSEKpHiFJNi4RYFGCAMNlOJhhBlBkesBMrMCrzYSomMAAAAASUVORK5CYII=[/img] dan sumbu [img width=9,height=18]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAXCAMAAADqZkX0AAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOpDbZgAAZmZmZpDbZrbbZrb/kDoAkDpmkNv/tmYAtmY6tmZmtv//25A625Bm2////7Zm/9uQ//+2///b+FnZRwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAYElEQVQoU7WPSxaAIAhFX1nZP7NSk9z/NvM7bhQjuAcuAPwdhjcKTlQdQAvxDXimMSx1IqBBxQOO9oaNGNBMuT1hWKYoY1Avr4y9Y/amFFFU8jLoa1M6TqmLA6Jevz5+Ael/BC1RMKIqAAAAAElFTkSuQmCC[/img] dengan [img width=35,height=18]data:image/png;base64,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[/img] dan [img width=36,height=18]data:image/png;base64,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[/img][br][br]