QSopt Format Example: Integer variables QSopt > Problem Formats > Examples
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The following LP format input defines an integer programming problem that contains four variables, each required to take on integer values, and three constraints. The first variable, x1, is bounded between 0 and 2, while the remaining three variables default to binary values, that is, they are bounded between 0 and 1.

Problem
 IntegerVars
Maximize
 obj: 4x1 + x2 + 5x3 + 3x4
Subject To
 r1:   x1 -  x2 -  x3 + 3x4 <= 1
 r2:  5x1 +  x2 + 3x3 + 8x4 <= 55
 r3:  -x1 + 2x2 + 3x3 - 5x4 <= 3
Bounds
 0 <= x1 <= 2
Integer
 x1 x2 x3
 x4 
End

The same problem is defined by the following MPS format input. It uses MARKER lines to specify that the four variables are required to take on integer values.

NAME    IntegerVars
OBJSENSE
  MAX
OBJNAME
  obj
ROWS
 N  obj
 L  r1
 L  r2
 L  r3
COLUMNS
 MARK0qs      'MARKER'    'INTORG'
  x1    obj    4   r3    -1   r2    5   r1    1
  x2    obj    1   r3     2   r2    1   r1   -1
  x3    obj    5   r3     3   r2    3   r1   -1
  x4    obj    3   r3    -5   r2    8   r1    3
 MARK4qs      'MARKER'    'INTEND'
RHS
 RHS    r1    1
 RHS    r2    55
 RHS    r3    3
BOUNDS
 UP BOUND    x1    2
ENDATA
 
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Last Updated: November 2003