Question: Xavier is a student who finds the simplex algorithm complicated and proposes the following alternative for finding an optimal solution to, max{cx : Ax =

Xavier is a student who finds the simplex algorithm complicated and proposes the following alternative for finding an optimal solution to, max{cx : Ax = b, x 0}. Using linear algebra find a maximal set of linearly independent columns AB whereB{1,...,n}.ThenAB isasquarematrix.Setxj =0forallj B and let xB be a solution to the system ABxB = b. Then x is a basic solution. Among all basic solution x , choose the one that maximizes cx. Discuss the merit of Xavier's proposals. In particular, indicate if the scheme always gives a correct answer, and if it is practical

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