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  1. max z = x1 - x2 + 3x3
    subject to
    x1 + x2 + x3 <= 10
    2x1 - x2 - x3 <= 2
    2x1 - 2x2 - 3x3 <= 6
    and x1,x2,x3 >= 0
  2. min z = 3x1 - 2x2 + 4x3
    subject to
    3x1 + 5x2 + 4x3 >= 7
    6x1 + x2 + 3x3 >= 4
    7x1 - 2x2 - x3 <= 10
    x1 - 2x2 + 5x3 >= 3
    4x1 + 7x2 - 2x3 >= 2
    and x1,x2,x3 >= 0
  3. min z = x1 + 2x2
    subject to
    2x1 + 4x2 <= 160
    x1 - x2 = 30
    x1 >= 10
    and x1,x2 >= 0
  4. min z = x1 - 3x2 - 2x3
    subject to
    3x1 - x2 + 2x3 <= 7
    2x1 - 4x2 >= 12
    -4x1 + 3x2 + 8x3 = 10
    and x1,x2 >= 0 and x3 unrestricted in sign
  5. max z = x1 - 2x2 + 3x3
    subject to
    -2x1 + x2 + 3x3 = 2
    2x1 + 3x2 + 4x3 = 1
    and x1,x2,x3 >= 0
  6. max z = 3x1 + x2 + 2x3 - x4
    subject to
    2x1 - x2 + 3x3 + x4 = 1
    x1 + x2 - x3 + x4 = 3
    and x1,x2 >= 0 and x3,x4 unrestricted in sign
 
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