Consider the kth iteration of the simplex method as defined in Algorithm 4.2 of the textbook. (a) Show that the matrix Ak+1, def
ined by replacing the sth row of Ak by the tth row of Ak is nonsingular. (The index t Wk is such that ak = σ, and the tth constraint is called a blocking constraint.) (b) Show that the component of the Lagrange multiplier λ, at xk+1 corresponding to the new constraint in the working set must be positive. (This implies that it is impossible to delete the constraint that was just added.)
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