The method of exterior forms by H. Grassmann and E. Cartan is used for solving the linear programming problem. It captures the essence of the problem in a convenient, compact form. The solution is presented by Cramer’s like rules and is reduced to computing the set of values of the objective function at the vertices of the polyhedron constraints, without any explicit calculation of the vertices themselves.
Bulletin of Mathematical Sciences and Applications (Volume 14)
G. V. Kondratiev "The Method of Exterior Forms in Linear Programming", Bulletin of Mathematical Sciences and Applications, Vol. 14, pp. 7-12, 2016