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Program Linear

Program Linear. Menyelesaikan Masalah Program Linear. Linear Program. Solving problem of linear program. y. 3. -2. 2. 1. x. 0. -1. 3. 1. -3. - 2. 2. Grafik Himpunan penyelesaian Sistem Pertidaksamaan Linear. Grafik Himpunan Penyelesaian Sistem Pertidaksamaan Linear

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Program Linear

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  1. Program Linear Menyelesaikan Masalah Program Linear

  2. Linear Program Solving problem of linear program

  3. y 3 -2 2 1 x 0 -1 3 1 -3 -2 2 Grafik Himpunan penyelesaian Sistem Pertidaksamaan Linear Grafik Himpunan Penyelesaian Sistem Pertidaksamaan Linear • Grafik Pertidaksamaan Linear Satu variabel Contoh : Tentukan daerah penyelesaian pertidaksamaan Jawab DP PROGRAM LINEAR

  4. y 3 -2 2 1 x 0 -1 3 1 -3 -2 2 Graph of solution set in Linear unequation system Graph of solution set in linear unequation system Graph of linear unequation in one variable Example : Determine the solution area of unequation Answer: DP PROGRAM LINEAR

  5. y 3 -2 2 1 x 3 -1 -3 -2 1 2 Grafik Himpunan penyelesaian Sistem Pertidaksamaan Linear 2.Tentukan daerah penyelesaian pertidaksamaan DP 0 PROGRAM LINEAR

  6. y 3 -2 2 1 x 3 -1 -3 -2 1 2 Graph of solution set in Linear unequation system 2.Determine the solution area of unequation DP 0 PROGRAM LINEAR

  7. Grafik Himpunan penyelesaian Sistem Pertidaksamaan Linear 1 2 1 2 3 2. Grafik Pertidaksamaan Linear dua Variabel y 1. Gambar 2x + 3y = 6 2. Mencoba titik DP x PROGRAM LINEAR Contoh 1 : Carilah daerah penyelesaian pertidaksamaan 2x + 3y < 6

  8. Graph of solution set in Linear unequation system 1 2 1 2 3 2. Graph of linear unequation in two variables y 1. Picture 2x + 3y = 6 2. Examining the point DP x PROGRAM LINEAR Example 1 : Find the solution area of unequation 2x + 3y < 6

  9. Grafik Himpunan penyelesaian Sistem Pertidaksamaan Linear 1 2 3 4 5 6 7 y 1. Gambar x + y = 7 2. Mencoba titik DP x PROGRAM LINEAR Contoh 2 : Carilah daerah penyelesaian pertidaksamaan x + y > 7

  10. Graph of solution set in Linear unequation system 1 2 3 4 5 6 7 y 1. Picture x + y = 7 2. Examining the point DP x PROGRAM LINEAR Example 2 : Find the solution area of unequation x + y > 7

  11. Grafik Himpunan penyelesaian Sistem Pertidaksamaan Linear y 1. Gambar x + y = 7 7 6 5 4 3 2 1 2. Gambar x + 2y = 10 3. Mencoba titik DP x 1 2 3 4 5 6 7 8 9 10 PROGRAM LINEAR Contoh 3 : Carilah daerah penyelesaian pertidaksamaan x + y > 7 dan x + 2y < 10

  12. Graph of solution set in Linear unequation system y 1. Picture x + y = 7 7 6 5 4 3 2 1 2. Picture x + 2y = 10 3. Examining the point DP x 1 2 3 4 5 6 7 8 9 10 PROGRAM LINEAR Example 3 : Find the solution area of unequation x + y > 7 and x + 2y < 10

  13. MODEL MATEMATIKA • Kompetensi Dasar : • Menentukan model matematika dari soal cerita • Indikator : • Soal cerita (kalimat verbal) diterjemakan ke kalimat matematika • Kalimat matematika ditentukan daerah penyelesaiannya PROGRAM LINEAR

  14. MATH MODEL • Base Competence : • Determining the math model from story test • Indicators : • Story test (verbal sentence) is translated into math sentence • Determining a solution area of math sentence PROGRAM LINEAR

  15. MODEL MATEMATIKA MEMBUAT MODEL MATEMATIKA • Perhatikan soal berikut ini : • Sebuah pesawat terbang mempunyai tempat duduk tidak lebih dari 300 kursi ,terdiri atas kelas ekonomi dan VIP • Penumpang kelas ekonomi boleh membawa bagasi 3 kg dan kelas VIP boleh membawa bagasi 5 kg sedangkan pesawat hanya mampu membawa bagasi 1200 kg, • Tiket kelas ekonomi memberi laba Rp 100.000.00 dan kelas VIP Rp 200.000,00 • Berapakah laba maksimum dari penjualan tiket pesawat tersebut ? PROGRAM LINEAR

  16. MATH MODEL MAKING MATH MODEL • See the exercise below : • A plane has not more than 300 seats, consist of economic and VIP class. • The passengers of economic class may bring about 3kg luggage and VIP class about 5kg luggage. While the plane is able to bring only 1200, • Ticket of economic class gives benefit Rp 100.000.00 and VIP class about Rp 200.000,00 • So how much is the maximum benefit of plane ticketing? PROGRAM LINEAR

  17. MODEL MATEMATIKA Pernyataan diatas dapat dubuat tabel sebagai berikut: Banyak kelas Ekonomi (x) Banyak kelas VIP (y) maximum x y 300 Tempat duduk Bagasi 3x 5y 1200 PROGRAM LINEAR

  18. MATH MODEL The statement above can be made two tables as follow: Economic class size (x) VIP class size (y) maximum x y 300 Seats Baggage 3x 5y 1200 PROGRAM LINEAR

  19. MODEL MATEMATIKA SISTEM PERTIDAKSAMAAN LINEAR PERMASALAHAN TERSEBUT ADALAH Pertidaksamaan (1) Pertidaksamaan (2) Pertidaksamaan (3) Pertidaksamaan (4) PROGRAM LINEAR

  20. MATH MODEL LINEAR UNEQUATION SYSTEM THE PROBLEMS ARE Unequation (1) Unequation(2) Unequation (3) Unequation (4) PROGRAM LINEAR

  21. NILAI OPTIMUM Melukis daerah himpunan penyelesaian sistem pertidaksamaan linier PROGRAM LINEAR

  22. OPTIMUM VALUE Drawing a solution set area Linear uneaquation system PROGRAM LINEAR

  23. x + y 300 NILAI OPTIMUM y 300 DP x 0 300 PROGRAM LINEAR

  24. x + y 300 OPTIMUM VALUE y 300 DP x 0 300 PROGRAM LINEAR

  25. 3x + 5y 1200 NILAI OPTIMUM y 240 DP x 400 0 PROGRAM LINEAR

  26. 3x + 5y 1200 OPTIMUM VALUE y 240 DP x 400 0 PROGRAM LINEAR

  27. NILAI OPTIMUM y x + y 300 3x + 5y 1200 300 240 (150, 150) DP x 300 400 0 PROGRAM LINEAR

  28. OPTIMUM VALUE y x + y 300 3x + 5y 1200 300 240 (150, 150) DP x 300 400 0 PROGRAM LINEAR

  29. x + y 300 • 3x + 5y 1200 • x 0 • y 0 NILAI OPTIMUM y 300 240 (150,150) DP X 0 300 400 PROGRAM LINEAR

  30. x + y 300 • 3x + 5y 1200 • x 0 • y 0 OPTIMUM VALUE y 300 240 (150,150) DP X 0 300 400 PROGRAM LINEAR

  31. NILAI OPTIMUM MENCARI NILAI OPTIMASI DENGAN UJI TITIK POJOK • x + y 300 • 3x + 5y 1200 y • x 0 • y 0 A(0,240) E(150,150) DP X 0 D(300,0) PROGRAM LINEAR

  32. OPTIMUM VALUE FINDING THE OPTIMUM VALUE BY CORNER POINT EXAMINATION • x + y 300 • 3x + 5y 1200 y • x 0 • y 0 A(0,240) E(150,150) DP X 0 D(300,0) PROGRAM LINEAR

  33. GARIS SELIDIK MENCARI NILAI OPTIMASI DENGAN GARIS SELIDIK y C(0,300) f : x + 2y A(0,240) A(0,240) E(150,150) DP x 0 D(300,0) B(400,0) f : x + 2y PROGRAM LINEAR

  34. INVESTIGATED LINE FINDIN THE OPTIMUM VALUE BY INVESTIGATED LINE y C(0,300) f : x + 2y A(0,240) A(0,240) E(150,150) DP x 0 D(300,0) B(400,0) f : x + 2y PROGRAM LINEAR

  35. NILAI OPTIMUM A Rp 30.000.000,00 MAAF MASIH SALAH B MAAF MASIH SALAH Rp 35.000.000,00 C MAAF MASIH SALAH Rp 45.000.000,00 HEBAT ANDABENAR D Rp48.000.000,00 PROGRAM LINEAR

  36. OPTIMUM VALUE A Rp 30.000.000,00 SORRY YOU ARE FALSE B SORRY, YOU’RE STILL FALSE Rp 35.000.000,00 C STILL FALSE Rp 45.000.000,00 GREAT! YOU’RE RIGHT D Rp48.000.000,00 PROGRAM LINEAR

  37. Soal program Linear : PROGRAM LINEAR Luas daerah parkir adalah 360 meter persegi. Luas rata-rata untuk sebuah mobil adalah 6 meter persegi, dan untuk sebuah bus adalah 24 meter persegi. Daerah parkir itu tidak dapat memuat lebih dari 30 kendaraan. Andaikan banyaknya mobil yang dapat ditampung adalah x dan banyaknya bus adalah y. Tentukan sistem pertidaksamaannya

  38. Exercise of Linear program: PROGRAM LINEAR Width of parking area is 360 meter square. The average width of a car is 6 meter square, and for the bus is about 24 meter square. The parking area cannot take more than 30 vehicles. If the car quantity is x and the number of bus is y. then determine the unequation system

  39. Selamat bekerja dan sukses selalu WASSALAM PROGRAM LINEAR TERIMA KASIH

  40. GOOD LUCK! PROGRAM LINEAR THANKS FOR THE ATTENTION

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