|
Feasible Solution Set:
Corner Point:
OR; Vertex:
A point of a solution region where two of its boundary lines intersect is called a corner point or vertex of the solution region.
Problem Constraint:
In a certain problem from everyday life each linear inequality concerning the problem is called the problem constraint.
Non – Negative Constraint
OR; Decision Variables:
The variables used in the system of linear inequalities relating to the problems of everyday life are non–negative and are called non–negative constraints or decision variables.
Feasible Region:
The solution region of an inequality restricted to the first quadrant is called the feasible region. In the case both 'x' and 'y' are always non–negative, i.e.  ,  .
Feasible Solution:
Each point of the feasible region is called the feasible solution of the system of linear inequalities.
Feasible Solution Set:
 A set consisting of all the feasible solutions of the system of linear inequalities is called feasiblesolution set.
Convex Region:
If the line segment joining any two point of a certain region lies entirely within the region, then such a region is called the convex region as shown in the figure.
Example:
Graph the feasible region of the system of linear inequalities.
Solution:
 ————— (A)
 ————— (B)
 ————— (C)
The corresponding equations of inequalities (A), (B) and (C), we get.
 ————— (1)
 ————— (2)
 ————— (3)
For x–Intercepts:
Put  in Eq (1), Eq (2) and Eq (3) we get
For y–Intercepts:
Put  in Eq (1), Eq (2) and Eq (3) we get
Test:
Put origin as test point in inequalities (A), (B) and (C).
|
|
|
|
|
 (True)
|
 (True)
|
 (True)
|
|
 Solution Set towards origin side.
|
 Solution Set towards origin side.
|
 Solution Set towards origin side.
|
To find the point of intersection of line  and  .
by solving eq (1) and (2)
4 Eq (1) – Eq (2)
  
  Put in (1)
  
   
   
 
This shows that the lines  and  intersect each other at 
From the above graph corner points are  ,  ,  ,  ,  .
| 
