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Bien Gabrielle Tupaz

What geometric condition occurs in a two-variable LP problem when multiple optimal solutions exist?

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Bernardo, Cyril James Z.
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Multiple optimal solutions occur in a two-variable linear programming problem when the objective function line lies completely parallel to an active boundary edge of the feasible region, meaning both the objective function and the binding constraint have the exact same slope. Instead of the objective line intersecting the feasible region at a single sharp corner point, it lies flush against an entire line segment connecting two adjacent optimal vertices. As a result, every single point along that shared boundary segment yields the same optimal value, giving the problem infinitely many optimal solutions instead of just one.

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Charlyne Memoriado
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In a two-variable linear programming problem, multiple optimal solutions occur when the objective function line is parallel to a binding constraint boundary that forms an edge of the bounded feasible region. As a result, the objective function achieves its optimal value along every point on that entire boundary line segment between two optimal extreme points (corner points) rather than at a single vertex.

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