Contoh Soal Program Linear
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Transcript of Contoh Soal Program Linear
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Program Linear
Alvin AnggriawanAulia Putri Srie Wardani
Denny FebrianLeony Chintya Arwinda
Siti Farah Azzura
Kelompok 5
Kelas XI MIA 1
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Soal
Seorang pedagang gorengan menjual pisang
goreng dan bakwan. Harga pembelian untuk satu
pisang goreng Rp. 1.000,00. Dan satu bakwan
Rp.400,00. Modalnya hanya Rp. 250.000,00 dan
muatan gerobak tidak melebihi 400 biji. Jika pisang
goreng dijual Rp. 1.300,00/biji dan bakwan dijual
Rp.600,00/biji. Maka, keuntungan maksimum yang
di peroleh adalah….
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Penyelesaian
• Untung :Pisang HJ-HB = Rp. 1300 – Rp.1000 = Rp. 300Bakwan HJ-HB = Rp. 600 – Rp.400 = Rp. 200
Pisang Goreng Bakwan Batas
Modal 1000 400 250.000
Muatan gerobak 400
Keuntungan 300 200 Maks.
Fungsi objektif 300x + 200y
1000x + 400y ≤ 250.000
x + y ≤ 400
x ≥ 0
y ≥ 0
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1000x + 400y ≤ 250.000100
= 10x + 4y ≤ 25002
5x + 2y = 1250
x 0 250
y 625 0
Uji titik (0,0)5x + 2y ≤ 12500 + 0 ≤ 1250
0 ≤ 1250(Benar)
5x + 2y ≤ 250.000
(x,y) (0,625)
(250,0)
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x + y = 400 Uji titik (0,0)x + y ≤ 4000 + 0 ≤ 400
0 ≤ 400(Benar)
x + y ≤ 400
x 0 400
y 400 0
(x,y) (0,400)
(400,0)
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Grafik
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Fungsi Objektif (300x + 200y)
Titik pojok (0,0) 300(0) + 200(0)
= Rp. 0
(250,0) 300(250) + 200(0) = 75.000 + 0 = Rp. 75.000
(0,400) 300(0) + 200(400) = 0 + 80.000 = RP. 80.000
(150,250) 300(150) + 200 (250) = 45.000 + 50.000 = Rp. 95.000
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Maka, keuntungan maksimumnya adalah
Rp.95.000,00Dengan menjual 150 pisang
goreng dan 250 bakwan.