Question

Exercise 4.22 Consider the dual simplex method applied to a standard form problem with linearly independent rows. Suppose that we have a basis which is primal infeasible, but dual feasible, and let i be such that xB(i) < 0. Suppose that all entries in the ith row in the tableau (other than xB(j)) are nonnegative. Show that the optimal dual cost is +oo.

Answer 1

the Simplex method terminates after a finite number of iterations
• at termination, we either have an optimal basis B or a direction δ such that Aδ = 0, δ ≥ 0, and cT δ < 0. In the former case, the optimal cost is finite, and in the latter case it has unbounded optimal cost of +∞.

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