If one uses the method of artificial variables in a problem without solution, this non-existence will become

Question:

If one uses the method of artificial variables in a problem without solution, this non-existence will become apparent by the fact that one cannot get rid of the artificial variable. Illustrate this by trying to maximize f = 2x1 + x2 subject to x1 > 0, x2 > 0, 2x1 + x2 < 2, x1 + 2x2 > 6, x1 + x2 < 4.