2 Linear Programming-Graphical Method.pptx

LPP graphical method

1. MCA 2020 1 st Semester January - April, 2021 Resourse Management Technique Dr. Dilip Kumar Yadav Professor Department of Computer Applications, National Institute of Technology Jamshedpur, India E mail :   [email protected]                LPP 2021

2. Linear Programming : Graphical Method LPP 2021 It presents graphical solution method for solving any LP problem with only two decision variables . An optimal as well as a feasible solution to an LP problem is obtained by choosing one set of values from several possible values of decision variables x1, x2, . . ., xn , that satisfies the given constraints simultaneously and also provides an optimal ( maximum or minimum ) value of the given objective function .

3. For LP problems that have only two variables, it is possible that the entire set of feasible solutions can be displayed graphically by plotting linear constraints on a graph paper in order to locate the best (optimal ) solution. The technique used to identify the optimal solution is called the graphical solution method (approach or technique) for an LP problem with two variables. Since most real-world problems have more than two decision variables, such problems cannot be solved graphically . However , graphical approach provides understanding of solving an LP problem algebraically, involving more than two variables LPP 2021

4. IMPORTANT DEFINITIONS LPP 2021

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11. Examples on Minimization LP Problem

12. Unbounded Solution

13. Since the given LP problem is of maximization, there exist a number of points in the shaded region for which the value of the objective function is more than 8. For example, the point (2, 2 )

14. Infeasible Solution An infeasible solution to an LP problem arises when there is no solution that satisfies all the constraints simultaneously . This happens when there is no unique (single) feasible region . This situation arises when a LP model that has conflicting constraints. Any point lying outside the feasible region violates one or more of the given constraints.

15. Solution The constraints are plotted on graph as usual as shown in Fig. 3.25. Since there is no unique feasible solution space, therefore a unique set of values of variables x 1 and x 2 that satisfy all the constraints cannot be determined. Hence, there is no feasible solution to this LP problem because of the conflicting constraints .

16. Thanks ? LPP 2021