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LINEAR PROGRAMMING

LINEAR PROGRAMMING. Example 1. Maximise I = x + 0.8 y subject to x + y  1000 2 x + y  1500 3 x + 2 y  2400. Initial solution: I = 0 at (0, 0). LINEAR PROGRAMMING. Example 1. Maximise I = x + 0.8 y subject to x + y  1000 2 x + y  1500

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LINEAR PROGRAMMING

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  1. LINEAR PROGRAMMING Example 1 Maximise I = x + 0.8y subject to x + y 1000 2x + y 1500 3x + 2y 2400 Initial solution: I = 0 at (0, 0)

  2. LINEAR PROGRAMMING Example 1 Maximise I = x + 0.8y subject to x + y 1000 2x + y 1500 3x + 2y 2400 Maximise I where I - x - 0.8y = 0 subject to x + y + s1= 1000 2x + y + s2= 1500 3x + 2y + s3= 2400

  3. SIMPLEX TABLEAU Initial solution I = 0, x = 0, y = 0, s1 = 1000, s2 = 1500, s3 = 2400

  4. PIVOT 1 Choosing the pivot column Most negative number in objective row

  5. PIVOT 1 Choosing the pivot element Ratio test: Min. of 3 ratios gives 2 as pivot element

  6. PIVOT 1 Making the pivot Divide through the pivot row by the pivot element

  7. PIVOT 1 Making the pivot Objective row + pivot row

  8. PIVOT 1 Making the pivot First constraint row - pivot row

  9. PIVOT 1 Making the pivot Third constraint row – 3 x pivot row

  10. PIVOT 1 New solution I = 750, x = 750, y = 0, s1 = 250, s2 = 0, s3 = 150

  11. LINEAR PROGRAMMING Example Maximise I = x + 0.8y subject to x + y 1000 2x + y 1500 3x + 2y 2400 Solution after pivot 1: I = 750 at (750, 0)

  12. PIVOT 2 Choosing the pivot column Most negative number in objective row

  13. PIVOT 2 Choosing the pivot element Ratio test: Min. of 3 ratios gives 0.5 as pivot element

  14. PIVOT 2 Making the pivot Divide through the pivot row by the pivot element

  15. PIVOT 2 Making the pivot Objective row + 0.3 x pivot row

  16. PIVOT 2 Making the pivot First constraint row – 0.5 x pivot row

  17. PIVOT 2 Making the pivot Second constraint row – 0.5 x pivot row

  18. PIVOT 2 New solution I = 840, x = 600, y = 300, s1 = 100, s2 = 0, s3 = 0

  19. LINEAR PROGRAMMING Example Maximise I = x + 0.8y subject to x + y 1000 2x + y 1500 3x + 2y 2400 Solution after pivot 2: I = 840 at (600, 300)

  20. PIVOT 3 Choosing the pivot column Most negative number in objective row

  21. PIVOT 3 Choosing the pivot element Ratio test: Min. of 2 ratios gives 1 as pivot element

  22. PIVOT 3 Making the pivot Divide through the pivot row by the pivot element

  23. PIVOT 3 Making the pivot Objective row + 0.4 x pivot row

  24. PIVOT 3 Making the pivot Second constraint row – 2 x pivot row

  25. PIVOT 3 Making the pivot Third constraint row + 3 x pivot row

  26. PIVOT 3 Optimal solution I = 880, x = 400, y = 600, s1 = 0, s2 = 100, s3 = 0

  27. LINEAR PROGRAMMING Example Maximise I = x + 0.8y subject to x + y 1000 2x + y 1500 3x + 2y 2400 Optimal solution after pivot 3: I = 880 at (400, 600)

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