Linked from
The 10 pages that link to Simplex algorithm, each with the reason it gives.
Linear programmingRelated: It searches the vertices where a linear objective can attain its optimum.
PolyhedronRelated: Its steps exploit the adjacency structure of polyhedral vertices.
Mathematical optimizationRelated: It exploits the geometry of linear objectives and constraints.
Farkas' lemmaRelated: Dual information produced by simplex methods can reveal infeasibility.