Consider the following optimization problemmaximise Z = −3|x1| + x2 subject to 2x1+x2≥2x1 − 2x2 ≥ −10 x1∈R, x2≥0.(a) Is this problem an LP problem in its current form? Explain your answer.(b) Convert this problem to an (equivalent) LP problem of the following form:Maximise Z = c⊤x subject to Ax = bwith x≥0, x∈Rnwhere c∈R^n, 0 ≤ b ∈ R^m and A is an m×n matrix, for some n and m.Explain every step you make. In particular, define every variable that you introduce and explain why it is needed.

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maximise

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter10: Inequalities

Section10.8: Systems Of Linear Inequalities

Problem 2E

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Question

Consider the following optimization problem

maximise Z = −3|x1| + x2 subject to 2x1+x2≥2

x1 − 2x2 ≥ −10 x1∈R, x2≥0.

(a) Is this problem an LP problem in its current form? Explain your answer.
(b) Convert this problem to an (equivalent) LP problem of the following form:

Maximise Z = c⊤x subject to Ax = b

with x≥0, x∈Rn

where c∈R^n, 0 ≤ b ∈ R^m and A is an m×n matrix, for some n and m.

Explain every step you make. In particular, define every variable that you introduce and explain why it is needed.

Expert Solution