GRAPHICAL METHOD

                GRAPHICAL METHOD

Linear Programming Problems involving two decision variables can easily be solved by 

Graphical Method. For Linear Programming Problems involving three or more variables, the 

graphical method is impossible

Solution Space

The region in the graph sheet which satisfies all the constraints including the non 

negativity restrictions is called the solution space.

 

No Solution

When there exists no solution space, there is no solution to the given L.P.P. This is when 

there is no common region corresponding to all the constraints.

Unique Solution

There is only one optimum solution for certain L.P.P is called Unique Solution.

 

Infinite Number of solution

Certain L.P.P have infinite number of optimum solution. In such case, the optimum value 

of Z is the same but the values of the decision variables x1, x2, x3,……..,differ.

 

Unbounded Solution

In some L.P.P the maximum value of Z occurs at the point at infinity only.

Following are the Major steps in the solution of L.P.P by Graphical Method.

Step:1 draw x1 and x2 axes (which are mutually perpendicular) on a graph sheet.

Step:2 draw a line and identity the region connected with its corresponding to each 

constraints.

Step:3 identity the solutions space which is the region that is common to all constraints 

including the non negative restrictions.

Step:4 find the value of Z at each vertex of the solution space.

Step:5 identity the optimum solution.

                                Thank You

VIKAS V

23UCM038

I B.Com

10.02.2024