Editing Simplex algorithm (section)

===Entering variable selection===
Since the entering variable will, in general, increase from 0 to a positive number, the value of the objective function will decrease if the derivative of the objective function with respect to this variable is negative. Equivalently, the value of the objective function is increased if the pivot column is selected so that the corresponding entry in the objective row of the tableau is positive.

If there is more than one column so that the entry in the objective row is positive then the choice of which one to add to the set of basic variables is somewhat arbitrary and several ''entering variable choice rules''<ref name="Murty66">{{harvtxt|Murty|1983|p=66}}</ref> such as [[Devex algorithm]]<ref>Harris, Paula MJ. "Pivot selection methods of the Devex LP code." Mathematical programming 5.1 (1973): 1–28</ref> have been developed.

If all the entries in the objective row are less than or equal to 0 then no choice of entering variable can be made and the solution is in fact optimal. It is easily seen to be optimal since the objective row now corresponds to an equation of the form 
:<math display="block">z(\mathbf{x})=z_B+\text{non-positive terms corresponding to non-basic variables}</math>

By changing the entering variable choice rule so that it selects a column where the entry in the objective row is negative, the algorithm is changed so that it finds the minimum of the objective function rather than the maximum.