3 Duality(3.1) Consider the following polyhedron in standard form:P = {x € R" : Ax = b,where A e Rmxn and b € Rm are given and x € Rn.(i) Consider the Phase 1 problem for solving (P):(P1) min{ea : Ax + a =b, x≥ 0, a ≥ 0},where a € Rm and e E Rm denotes the vector of all ones, i.e., e = [1,1, ..., 1]T. Writedown the dual of (P1), explaining clearly each step in your solution.(ii) Prove that the dual of (P1) has a finite optimal value.(3.2) Determine the set of all optimal solutions for the following linear program using the graphicalmethod:(P)mins.t.X1 + X2 +X1X2+X1 +2x2X1x2x ≥ 0},Suppose that b ≥ 0."9x3X32x3x3-X4X42x4X4==≥ 0.

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Answered: Prove that the dual of (P1) has a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Prove that the dual of (P1) has a finite optimal valı