( iii ) The polygonal region so obtained , satisfying all the constraints and the non-negative restrictions is the convex set of all feasible solutions of the given LPP , which is also known as feasible region .
( iv ) Determine the extreme points of the feasible region .
( v ) Give some convenient value k to the objective function Z and draw the corresponding straight line in the xy-plane .
( vi ) If the problem is of maximization , then draw lines parallel to the line Z = k and obtain a line which is farthest from the origin and has atleast one point common to the feasible region . If the problem is of minimization , then draw lines parallel to the line Z = k and obtain a line , which is nearest to the origin and has atleast one point common to the feasible region .
( vii ) The common point so obtained is the optimal solution of the given LPP .
Working Rule for Marking Feasible Region Consider the constraint ax + by ≤ c , where c > 0 .
First draw the straight line ax + by = c by joining any two points on it . For this find two convenient points satisfying this equation .
This straight line divides the xy-plane in two parts . The inequation ax + by c will represent that part of the xy-plane which lies to that side of the line ax + by = c in which the origin lies .
Again , consider the constraint ax + by ≥ c , where c > 0 . Draw the straight line ax + by = c by joining any two points on it .
This straight line divides the xy-plane in two parts . The inequation ax + by ≥ c will represent that part of the xy-plane , which lies to that side of the line ax + by = c in which the origin does not lie .
Important Points to be Remembered
( i ) Basic Feasible Solution A BFS is a basic solution which also satisfies the non-negativity restrictions .
( ii ) Optimum Basic Feasible Solution A BFS is said to be optimum , if it also optimizes ( Max or min ) the objective function .