Corner Point Method is an important one to solve linear Programming Problems.
Following are the method comprises of the following steps:
(i) Find the feasible region of the linear programming problem and determine
its corner points (vertices).
(ii) Evaluate the objective function Z = ax + by at each corner point. Let M
and m respectively be the largest and smallest values at these points.
(iii) If the feasible region is bounded, M and m respectively are the maximum
and minimum values of the objective function.
If the feasible region is unbounded, then
(i) M is the maximum value of the objective function, if the open half plane
determined by ax + by > M has no point in common with the feasible
region. Otherwise, the objective function has no maximum value.
(ii) m is the minimum value of the objective function, if the open half plane
determined by ax + by < m has no point in common with the feasible
region. Otherwise, the objective function has no minimum value.
Following are the method comprises of the following steps:
(i) Find the feasible region of the linear programming problem and determine
its corner points (vertices).
(ii) Evaluate the objective function Z = ax + by at each corner point. Let M
and m respectively be the largest and smallest values at these points.
(iii) If the feasible region is bounded, M and m respectively are the maximum
and minimum values of the objective function.
If the feasible region is unbounded, then
(i) M is the maximum value of the objective function, if the open half plane
determined by ax + by > M has no point in common with the feasible
region. Otherwise, the objective function has no maximum value.
(ii) m is the minimum value of the objective function, if the open half plane
determined by ax + by < m has no point in common with the feasible
region. Otherwise, the objective function has no minimum value.
