Discussion
Which one of the following statements is TRUE?
Answer: D
The true statement is A linear programming problem can have a non-basic optimal solution.
When an LP has two optimal basic feasible solutions, every point on the segment joining them is also optimal, because the objective is linear. The interior points of that segment are optimal but not basic.
The others are false. A convex set can have infinitely many extreme points: every point of a circle is an extreme point of a closed disc. The feasible region of an LP is a polyhedron, which has only finitely many extreme points, since each is fixed by a choice of basis. And if an LP has two different optimal solutions, it has infinitely many (the whole segment between them), so it can never have exactly two.
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