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Mathematical Problems in Engineering
Volume 2017, Article ID 2742540, 11 pages
https://doi.org/10.1155/2017/2742540
Research Article

On Best Corrected Mixture Problems in Metallurgy: A Case Study

Département de Mathématiques, Université de Sherbrooke, 2500 Boulevard de l’Université, Sherbrooke, QC, Canada J1K 2R1

Correspondence should be addressed to F. Dubeau; ac.ekoorbrehsu@uaebud.siocnarf

Received 15 October 2016; Revised 28 January 2017; Accepted 30 January 2017; Published 27 February 2017

Academic Editor: Risto Lahdelma

Copyright © 2017 F. Dubeau and M. E. Ntigura Habingabwa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider three simple mixture problems occurring in metallurgy. The first problem considered is the classic minimum cost mixture problem. For the second problem, we consider finding a correction to a given mixture, a premix, without considering the cost of this premix. We only consider the cost and the weight of the quantity used as a correction. We show that the minimum cost correction does not correspond to the minimum weight correction, and we built the Pareto curve that gives all intermediate solutions between these two extreme solutions. Finally, the third problem is the correction problem for a nonfree premix. The correction is done to obtain a minimum cost corrected mixture.