Answered: Solve the standard minimization problem…

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

Solve the standard minimization problem using duality. (You may already have seen some of them in earlier sections, but now you will be solving them using a different method.)

Minimize c = s + t subject to

s + 8t ≥ 54
8s + t ≥ 54
s ≥ 0, t ≥ 0.

c=(s, t)

Expert Solution

Step 1

First we have to convert problem into a tableau it would look like A matrix.

The first step in solving a standard minimization problem using duality is to write information into a matrix ,ignoring everything you know about slack variable and objective function.

Fortunately , a standard minimization problem can be converted into maximization problem with same solution. The minimization problem are called duals of each other.

Standard minimization form :- if we convert standard minimization problem to straight into tableau it would look like

$[\begin{matrix} \end{matrix}]$ 3x6