My question is: is optimal solution exsit in case of infeasibilty? I am confused becz in my book ..it said..optimal solution exist but artificial variable not eliminated from table(infeasible case).
But its definition of optimal solution that it must be a feasible solution first.
Both contradicting each other.
An optimal solution must be feasible, so infeasible and optimal are mutually exclusive. What can happen with the two-phase simplex method, however, is that an artificial variable remains in the final basis when an optimal solution is found. In such a case, the basic artificial variable must equal zero. In other words, the final tableau contains a row where the right-hand side value is zero and the basic variable in that row is artificial. The zero-valued artificial variable does not prevent the overall solution from being feasible.
