Constraints
1) A constraint of the type ≤ (≥) can be converted to an equation by adding a slack variable to (subtracting a surplus variable form) the left side of the constraint.
For illustration, in the constraint: X_{I} + 2X_{2} ≤ 6 we add a slack S_{I} ≥ 0 to the left side to obtain the equation: X_{I }+ 2X_{2} + S_{I} = 6, S_{I} ≥ 0.
If the constraint represents the limit on the usage of a resource, S_{I} will represent the slack or unused amount of the resource.
After that consider the constraint: 3X_{I} + 2X_{2} - 3X_{3} ≥ 5, we subtract a surplus variable S_{2} ≥ 0 from the left side to obtain the equation.3X_{I} + 2X_{2} - 3X_{3} - S_{2} = 5, S_{2} ≥ 02) The right side of an equation can always be made non-negative by multiplying both sides by -1.
For illustration, 2X_{I} + 3X_{2} - 7X_{3} = -5 is mathematically equivalent to -2X_{I} - 3X_{2} + 7X_{3} = +5.3) The direction of an equation is reversed when both sides are multiplied by -1. For illustration, whereas 2 < 4, -2 > -4. Thus the inequality 2X_{I} - X_{2} ≤-5 can be replaced by -2X_{I} + X_{2} ≥ 5.