Consider the following LP max x1 + x2 s.t. x1 −x2 ≤2 (y1) −2x1 + 3x2 ≤2 (y2) −x1 −2x2 ≤−1 (y3) x1, x2 ≥0 1. Write down the dual of the primal LP. 2. Based on complementary slackness, argue whether x1 = 2, x2 = 2 is an optimal solution to the primal LP.

Consider the following LP max x1 + x2 s.t. x1 −x2 ≤2 (y1) −2x1 + 3x2 ≤2 (y2) −x1 −2x2 ≤−1 (y3) x1, x2 ≥0 1. Write down the dual of the primal LP. 2. Based on complementary slackness, argue whether x1 = 2, x2 = 2 is an optimal solution to the primal LP.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Consider the following LP
max x1 + x2
s.t. x1 −x2 ≤2 (y1)
−2x1 + 3x2 ≤2 (y2)
−x1 −2x2 ≤−1 (y3)
x1, x2 ≥0
1. Write down the dual of the primal LP.
2. Based on complementary slackness, argue whether x1 = 2, x2 = 2 is an optimal solution to the primal
LP.

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