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

The method used to solve Linear Programming Problems (LPP) without the use of artificial variables is called the Big M Method. This method is particularly useful when dealing with constraints that require artificial variables for the initial feasible solution.

In the Big M Method, a large positive constant, denoted by "M," is incorporated into the objective function to penalize the inclusion of artificial variables. This process ensures that when the solution is optimized, the artificial variables are driven out of the solution, ideally resulting in a feasible solution to the original problem.

The Big M Method is beneficial in situations where constraints have to maintain specific conditions without the assist of artificial variables. It streamlines the process of finding an optimal solution, making it a vital technique in linear programming. Moreover, this method is favored for its straightforwardness and efficiency in handling LPPs with equality constraints and surplus variables.