Any linear programming problem involving two variables can be easily solved with the help of graphical method as it is easier to deal with two dimensional graph. All the feasible solutions in graphical method lies within the feasible area on the graph and we used to test the corner points of the feasible area for the optimal solution i.e. one of the corner points of the feasible area used to be the optimal solution. We used to test all the corner points by putting these value in objective function.

Simplex method of solving linear programming problem uses only the corner points of the feasible region.

The simplex method is an iterative procedure used to solve linear programming problems. It starts at one of the corner points of the feasible region and moves from one corner point to another in order to find the optimal solution.

Feasible Region:
The feasible region is the set of all points that satisfy all the constraints of the linear programming problem. It is represented graphically as a bounded area in the coordinate plane.

Corner Points:
Corner points, also known as vertices, are the extreme points of the feasible region. Each corner point represents a specific combination of decision variables that satisfy all the constraints. The simplex method starts at one of these corner points and moves along the edges of the feasible region to find the optimal solution.

Explanation:
The simplex method uses only the corner points of the feasible region because these points are the only ones that need to be considered in order to find the optimal solution. This is due to the linearity of the objective function and constraints in a linear programming problem.

When the simplex method starts at a corner point, it evaluates the objective function at that point. It then moves to an adjacent corner point that improves the objective function value. This process continues until no further improvement can be made, indicating that the optimal solution has been reached.

Since the feasible region is a convex polygon in a linear programming problem, any point within the feasible region can be represented as a convex combination of the corner points. Therefore, considering any other points within the feasible region would be redundant and unnecessary in finding the optimal solution.

By using only the corner points, the simplex method efficiently explores the feasible region and converges to the optimal solution in a finite number of iterations. This makes it a powerful and widely used algorithm for solving linear programming problems.

In conclusion, the simplex method of solving linear programming problems uses only the corner points of the feasible region because these points represent the extreme combinations of decision variables that satisfy all the constraints. Considering other points within the feasible region is unnecessary and redundant in finding the optimal solution.

Where is the answer?