maximise

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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Consider the following optimization problem

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

x1 − 2x2 ≥ −10 x1∈R, x2≥0.

  1. (a)  Is this problem an LP problem in its current form? Explain your answer.

  2. (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.

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