The method used to solve LPP with out the use of artificial variables is called the .............. method.ans.

The method used to solve Linear Programming Problems (LPP) without the use of artificial variables is called the Big M Method or sometimes referred to simply as the Simplex Method in certain contexts.

In the context of linear programming, the Big M Method incorporates a large constant (M) to penalize the use of artificial variables. This method is particularly useful when the goal is to find feasible solutions that may not explicitly satisfy all constraints from the start. By assigning a large cost to the artificial variables, the algorithm effectively drives them out of the solution as the optimization progresses, leading to a feasible and optimal solution to the original problem.

Thus, the correct answer to the question is "Big M Method."