Corner points represent:

Question

BlackTom AI · Accepted Answer

Let’s parse the question and the options to understand what corner points typically represent in the context of optimization and feasible regions.
Option 1: 'A point outside of the feasible region' — This is incorrect because corner points are defined by being on the boundary of the feasible region, where constraints are satisfied. A point outside the feasible region violates at least one constraint, so it cannot be a corner of the feasible set.
Option 2: 'Infeasibility' — Infeasibility means there is no point that satisfies all the constraints simultaneously. A corner point, by definition, is a feasible point that lies at the intersection of constraint boundaries, so it cannot represent infeasibility. This option misinterprets what a corner point is.
Option 3: 'A point at which a set of constraints intersect' — This aligns with the standard geometric interpretation: a corner (or vertex) occurs where two or more constraint boundaries meet, forming a corner of the feasible region. It is precisely the intersection of constraint lines or planes that defines corners.
Option 4: 'The intersection of the axes' — This describes a specific, often incidental point (like the origin) and does not capture the general concept of corner points in a constrained region. Corners are about constraint intersections, not necessarily the coordinate axes themselves.
In summary, the concept of a corner point is best captured by a point where multiple constraints intersect, because that is where the feasible region changes direction and a vertex is formed. The other options describe situations that either fall outside the feasible region, indicate infeasibility, or reference a special case that does not define corner points in general.

BUSOBA 2321 SP2025 (4947) Quiz 7 - Replacement for Quiz 4

Corner points represent:

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