What is meant by "alternative optimal solutions" in linear programming?

The concept of "alternative optimal solutions" in linear programming refers to scenarios where there are multiple feasible solutions that achieve the same optimal objective value. This means that there is not just one unique solution that maximizes or minimizes the objective function, but rather a set of solutions that can be equally effective in terms of the objective outcome.

In a linear programming context, this typically occurs when the objective function is parallel to a constraint line in the feasible region. When this happens, any point along this line segment may provide the same maximum or minimum value for the objective function, thus creating a situation where multiple optimal solutions exist.

For example, if the optimal cost of producing a certain quantity of goods is the same at two different combinations of resource allocations, both combinations are considered alternative optimal solutions as they lead to the same result while adhering to constraints of the problem.

The other choices do not accurately describe alternative optimal solutions. Infeasible solutions do not meet the constraints of the problem and cannot be considered optimal. Solutions that yield no value or violate constraints are not viable options in linear programming and thus are not relevant when discussing optimality.