**What are the Constraints?**

*Constraints* define the possible values the variables
of a linear programming problem may take. They typically represent
resource constraints, or the minimum or maximum level of some
activity. They take the following general form:

where

X= the_{i}i^{th}decision variable,

a_{j, i }_{}= the coefficient onXin constraint_{i}j, and

b= the right-hand-side coefficient on constraint_{j}j.

Note that *j* is an index that runs from 1 to *m*,
and each value of *j* corresponds to a constraint. Thus,
the above expression represents *m* constraints (equations,
or, more precisely, inequalities) with this form. Resource constraints
are a common type of constraint. In a resource constraint, the
coefficient *a _{j, i }*

Note also that while the constraint above is written as a less-than-or-equal constraint, greater-than-or-equal constraints can also be used. A greater-than-or-equal constraint can always be converted to a less-than-or-equal constraint by multiplying it by -1. Similarly, equality constraints can be written as two inequalities -- a less-than-or-equal constraint and a greater-than-or-equal constraint.

Back to Section 1