Why do we introduce artificial variable in two phase simplex method?

Question

In two phase simplex method we use artificial variables when our constraint is greater than or equal to some constant. I just want to know what is the purpose of these artificial variables?

Answer 1

To use the simplex algorithm we need our LP in standard form $\textbf{maximise } f=\bar c^{T}\bar x$ subject to $A\bar x=\bar b$ and $\bar x\geq 0$. The reason for introducing slack variables is solely to convert the constraints $A\bar x\leq\bar b$ to the standard form $A\bar x=\bar b$ so that we can apply the simplex algorithm.

Answer 2

I got my answer from other source. It clears all my confusion.

The general idea behind two-phase methods is create an auxiliary problem, with an obvious starting solution (which may be infeasible for the original problem), and with the objective of eliminating the infeasibilities. If the optimal auxiliary solution eliminates the infeasibilities, then the auxiliary solution values of the variables from the original problem can be used to start phase 2 with a basic feasible solution.

The artificial variables in phase 1 are introduced so that we can make the original problem variables nonbasic and set them to zero even though that may not be feasible to the original problem. The artificial variables take on the resulting infeasibilities and are basic at the start of phase 1. The phase 1 objective is to drive those variables to zero, at which point the original problem variables are feasible and the current basis consists of original problem variables. (Some minor cleanup may be necessary in the case of degeneracy.) Then one can use that basis as the start of phase 2.

If one can’t drive all the artificials to zero, that means the original problem has no feasible solution