Lesson plan
Basic feasible solution
In the theory of linear programming, a basic feasible solution (BFS) is a solution with a minimal set of non-zero variables. Geometrically, each BFS corresponds to a vertex of the polyhedron of feasible solutions. If there exists an optimal solution, then there exists an optimal BFS. Hence, to find an optimal solution, it is sufficient to consider the BFS-s. This fact is used by the simplex algorithm, which essentially travels from one BFS to another until an optimal solution is found.
Article summary
In the theory of linear programming, a basic feasible solution (BFS) is a solution with a minimal set of non-zero variables. Geometrically, each BFS corresponds to a vertex of the polyhedron of feasible solutions. If there exists an optimal solution, then there exists an optimal BFS. Hence, to find an optimal solution, it is sufficient to consider the BFS-s. This fact is used by the simplex algorithm, which essentially travels from one BFS to another until an optimal solution is found.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
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- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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