show that if the optimal value of the objective function of a linear programming problem is attained at several extreme points, then it is also attained at any convex combination of these extreme points.
As the feasible region is a convex closed polytope the line segment between any two of the points where the objective attains its maximum is in the feasible region.
As the objective is linear :
Then, if , and and are points where the objective attains its optimum value, then is feasible and:
so would the question here actually be pertaining to the case when the maximum is attained at two points instead of "several" points? and also, when you say Ob(λx+(1-λ)y) does this represent the arbitrary convex combination of two extreme pts? (i know this might be a stupid question)