What does it signify if a linear programming model has multiple extreme points?

The correct choice indicates that having multiple extreme points in a linear programming model can signify the presence of more than one optimal solution. In linear programming, an extreme point, or vertex, of the feasible region represents a potential solution to the optimization problem. When the objective function is evaluated at these vertices, if multiple extreme points yield the same optimal value, it means that the optimal solution is not unique.

This situation commonly arises in cases where the objective function is parallel to a constraint that forms part of the feasible region. The existence of multiple extreme points that yield the same objective function value allows for different combinations of decision variables to be optimal, providing flexibility in solution choice.

This characteristic is fundamental in linear programming, as it illustrates the potential for alternative feasible solutions that meet the same optimal outcome, thereby allowing decision-makers to select solutions based on additional criteria such as preference, cost, or resource allocation.

The other options do not align with this principle. For instance, stating that every extreme point is an infeasible solution contradicts the definition of extreme points, which are found within the feasible region. Similarly, implying that the constraints have not been properly defined or that there is a need for adjustment in the decision variables does not necessarily follow from the presence of multiple