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GRAPHICAL METHOD

GRAPHICAL METHOD. Graphical method can be applied to LPP with two variables. The entire set of feasible solution( feasible region) can be displayed graphically by plotting linear constraints on a graph paper to locate the optimal solution. DEFINITIONS.

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GRAPHICAL METHOD

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1. GRAPHICAL METHOD

2. Graphical method can be applied to LPP with two variables. • The entire set of feasible solution( feasible region) can be displayed graphically by plotting linear constraints on a graph paper to locate the optimal solution.

3. DEFINITIONS • Solution is the set of values of decision variables(x1 , x2…. xn) which satisfy the constraints of an LP problem . • Feasible Solution is a solution for which all the constraints are satisfied. • Infeasible Solution is a solution for which atleast one constraint is violated. • Feasible Region is the collection of all feasible solutions.

4. Optimal Solution is a feasible solution that has the most favourablevalue of the objective function. • Most favourable value is the largest value if the objective function is to be maximised, and is the smallest value if the objective function is to be minimized. • Corner-Point feasible (CPF) solution is a solution that lies at a corner of the feasible region.

5. PROCEDURE • Write the problem in mathematical form • Write the inequality constraints as equality constraints. • Draw the graph. • Identify the feasible region or solution space. • Locate the corner points or vertices of the feasible region. • Evaluate the objective function at the corner points . • Find the optimum value of the objective function.

6. Multiple optimal solution : LPP attains optimality at more than one corner point of the feasible region. • Unbounded Solution : One or more decision variable will increase indefinitely without violating feasibility and thus the value of the objective function can be increased or decreased indefinitely. • Infeasible Solution ( no solution) : All the constraints cannot be satisfied simultaneously.

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