it must occur at a corner point of R. (By Theorem ). In the above example, the corner points (vertices) of the bounded (feasible) region are: O, A, B and C and it is easy to find their coordinates as ( , ), ( , ), ( , ) and ( , ) respectively. Let us now compute the values of Z at these points.
We have * A corner point of a feasible region is a point in the region which is the intersection of two boundary lines. ** A feasible region of a system of linear inequalities is said to be bounded if it can be enclosed within a circle. Otherwise, it is called unbounded. Unbounded means that the feasible region does extend indefinitely in any direction.
Vertex of the Corresponding value Feasible Region of Z (in Rs) O ( , ) C ( , ) B ( , ) A ( , ) Maximum LINEAR PROGRAMMING We observe that the maximum profit to the dealer results from the investment strategy ( , ), i.e. buying tables and chairs. This method of solving linear programming problem is referred as Corner Point Method . The method comprises of the following steps: .
Find the feasible region of the linear programming problem and determine its corner points (vertices) either by inspection or by solving the two equations of the lines intersecting at that point. . Evaluate the objective function Z = ax + by at each corner point. Let M and m , respectively denote the largest and smallest values of these points.
. (i) When the feasible region is bounded , M and m are the maximum and minimum values of Z. (ii) In case, the feasible region is unbounded , we have: . (a) M is the maximum value of Z, if the open half plane determined by ax + by > M has no point in common with the feasible region.
Otherwise, Z has no maximum value. (b) Similarly, m is the minimum value of Z, if the open half plane determined by ax + by < m has no point in common with