We need to use the non-standard simplex method whenever there is a negative constant to the right of one or more ≤ constraints.

Alternatively, set up the initial simplex tableau. If there are one or more negative constants above the horizontal line, then we need to use the non-standard simplex method.

• Answer

If one (or more) constraints are an equation (rather than an inequality), we create two inequalities out of the equation. 

For example, if we have the equation 2x + y = 7, then this equation is true when both 2x + y ≤ 7 and 2x + y ≥ 7. Since the second inequality is going "in the wrong direction," we multiply both sides by -1 to "flip" the inequality. This gives us: -2x - y ≤ -7. 

In this way, we turn the equation 2x + y = 7 into two inequalities:

• 2x + y ≤ 7

• -2x - y ≤ -7

(A consequence of this is that we always need to use the non-standard simplex method whenever solving a linear programming problem with an equality constraint.)