The Two Phase Method is a problem-solving technique used in linear programming to solve problems with multiple constraints and variables. It involves breaking down the problem into two phases: the first phase is used to find an initial feasible solution, and the second phase is used to optimize the solution.
The Two Phase Method is used when a linear programming problem has constraints that cannot be easily satisfied or when there are multiple optimal solutions. It is also used when the problem has a mix of equality and inequality constraints.
The objective of the Two Phase Method is to find the optimal solution that maximizes the objective function while satisfying all the constraints of the problem. The first phase of the method aims to find an initial feasible solution, and the second phase aims to improve and optimize that solution.
The first step is to convert the problem into standard form by adding slack or surplus variables. Then, in the first phase, a starting basic feasible solution is found using the simplex method. In the second phase, the simplex method is used to optimize the solution found in the first phase. Finally, the optimal solution is obtained.
The Two Phase Method is useful for solving linear programming problems with many constraints and variables. It also allows for the handling of both equality and inequality constraints in a problem. Additionally, it guarantees an optimal solution, even if the problem has multiple optimal solutions.