Note The solution set of simultaneous linear inequations may be an empty set or it may be the region bounded by the straight lines corresponding to given linear inequations or it may be an unbounded region with straight line boundaries .
Graphical Method to Solve a Linear Programming Problem There are two techniques of solving a LPP by graphical method 1 . Corner point method and 2 . Iso-profit or Iso-cost method
1 . Corner Point Method
This method of solving a LPP graphically is based on the principle of extreme point theorem .
Procedure to Solve a LPP Graphically by Corner Point Method ( i ) Consider each constraint as an equation .
( ii ) Plot each equation on graph , as each one will geometrically represent a straight line .
( iii ) The common region , thus obtained satisfying all the constraints and the non-negative restrictions is called the feasible region . It is a convex polygon .
( iv ) Determine the vertices ( corner points ) of the convex polygon . These vertices are known as the extreme points of corners of the feasible region .
( v ) Find the values of the objective function at each of the extreme points . The point at which the value of the objective function is optimum ( maximum or minimum ) is the optimal solution of the given LPP .
2 . Isom-profit or Iso-cost Method
Procedure to Solve a LPP Graphically by Iso-profit or Iso-cost Method
( i ) Consider each constraint as an equation .
( ii ) Plot each equation on graph as each one will geometrically represent a straight line .