Field 1 in a RHS or RANGES data line is a (possibly empty) label. The parser ignores RHS and RANGES data lines with a label that differs from the label used in the section's first data line. (This convention makes it possible to study several different models with minimal change to the input; it arose in the days when data was described via card decks.)

RHS and RANGES data lines contain a row name on field 2, and a floating point value in field 3. Additional row name, number pairs may follow on fields 4 and 5, fields 6 and 7, etc. Each row may be mentioned at most once in a RHS data line, and at most once in a RANGES data line.

In the absence of a RANGES definition for a row, the row's right-hand-side either defaults to 0.0 or assumes the value given in its RHS data line. A constraint's RANGES definition states that the constraint's expression must evaluate to a number that falls within an interval that depends on the constraint's right-hand-side and the range value, as well as the constraint's sense. If rhs is a constraint's right-hand-side value and range is the constraint's range value, then the range interval is defined according to the following table:

The MPS input excerpt

            ROWS
              N  obj
              L  lower
              G  greater
              E  equal
            RHS 
              rhs lower 10

            RANGES 
              lower    8
              greater -5
              equal   -0.5

• lower's constraint expression falls inside the interval [2.0, 10.0]
• greater's constraint expression falls inside the interval [0.0,5.0]
• equal's constraint expression falls inside the interval [-0.5,0.0]

See also MPS format definition and MPS format sections.