If an LP has multiple optimal solutions, must all of them be corner points? Explain.
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No. Only the extreme optimal solutions are corner points. If multiple optimal solutions exist, every point along the line segment between optimal corner points is also optimal, including non-corner points.
No, not all optimal solutions must be corner points. When a linear program has multiple optimal solutions, it possesses an infinite number of optimal solutions located along the entire line segment, face, or edge connecting two or more optimal corner points.
No. If an LP has multiple optimal solutions, the optimal solutions can include an entire line segment or edge of the feasible region. The endpoints of that segment are corner points (extreme points) and are optimal, but the points between them are also optimal even though they are not corner points. Thus, at least two corner points can be optimal, while infinitely many points between them may also be optimal.
No. Multiple optimal solutions do not have to all be corner points; if two corner points are optimal, every point on the line segment connecting them is also optimal, including non-corner points.
No, if a linear programming (LP) problem has multiple optimal solutions, they do not all have to be corner points.
No. Not all optimal solutions have to be corner points. When multiple optimal solutions exist, every point along the line segment between two optimal corner points is also optimal, so many optimal solutions can be non-corner points.
No, not all optimal solutions must be corner points (extreme points).
No. If an LP has multiple optimal solutions, the corner points at the ends of the optimal edge are optimal, but every point along the line segment between them is also optimal. Therefore, some optimal solutions are corner points, while the points between those corners are not corner points but still have the same optimal objective value.
No. Not all optimal solutions must be corner points. In an LP with multiple optimal solutions, the optimal solutions can include all points along an edge or line segment between two optimal corner points. The corner points are optimal, but the points between them can also have the same optimal objective value.
No, not all optimal solutions must be corner points. In an LP with multiple optimal solutions, the corner points at the ends of the optimal edge are optimal, but every point between those corner points is also optimal. This happens when the objective function is parallel to a binding edge of the feasible region, so the entire line segment can have the same optimal objective value.
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