Consider the following linear programming problem (P) in standard form: (P) min{c"x : Ax = b, x > 0}, where A E Rmxn¸ b€ R™, and c e R". Let ī E R" be a vertex of the feasible region of (P). (4.2) Let...

0}, where A E Rmxn¸ b€ R™, and c e R". Let ī E R" be a vertex of the feasible region of (P). (4.2) Let d e R" be a feasible direction at such that d + 0. Prove that –d e R" is not a feasible direction at . (Hint: Consider the effect of the hypothesis d+0 on the subvector dN, where BC {1,..., n} and N C {1,.. , n} denote the corresponding index sets of the vertex ē.) "/>
Extracted text: Consider the following linear programming problem (P) in standard form: (P) min{c"x : Ax = b, x > 0}, where A E Rmxn¸ b€ R™, and c e R". Let ī E R" be a vertex of the feasible region of (P). (4.2) Let d e R" be a feasible direction at such that d + 0. Prove that –d e R" is not a feasible direction at . (Hint: Consider the effect of the hypothesis d+0 on the subvector dN, where BC {1,..., n} and N C {1,.. , n} denote the corresponding index sets of the vertex ē.)