Which concept describes a point where linear functions do not intersect?

The concept that describes a point where linear functions do not intersect is known as infeasibility. In linear programming, a feasible region is defined by the set of all points that satisfy the constraints of the problem, represented by linear inequalities. If two or more constraints are such that they create an area with no common solutions—meaning there's no point that satisfies all the constraints simultaneously—this situation is referred to as infeasibility.

Infeasibility highlights the absence of a solution within the defined constraints, indicating that the linear functions representing those constraints do not intersect within the specified domain, thus preventing the existence of any viable combinations that meet all conditions.

The other concepts listed serve different roles in linear programming. The feasible region itself encompasses all possible solutions that adhere to the constraints, whereas extreme points refer to the vertices of the feasible region where optimal solutions can be found. An optimal solution is the best outcome that maximizes or minimizes the objective function within the feasible region. However, when those functions do not intersect due to infeasibility, no solutions exist, and thus the focus shifts to understanding the problems arising from such constraints.