<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1405-7743</journal-id>
<journal-title><![CDATA[Ingeniería, investigación y tecnología]]></journal-title>
<abbrev-journal-title><![CDATA[Ing. invest. y tecnol.]]></abbrev-journal-title>
<issn>1405-7743</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Facultad de Ingeniería]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1405-77432005000100047</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Introducción suave a ideas fundamentales para resolver problemas de programación lineal en enteros por medio de matemáticas recreativas]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Murray-Lasso]]></surname>
<given-names><![CDATA[M.A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,UNAM Facultad de Ingeniería División de Estudios de Posgrado]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>03</month>
<year>2005</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>03</month>
<year>2005</year>
</pub-date>
<volume>6</volume>
<numero>1</numero>
<fpage>47</fpage>
<lpage>58</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1405-77432005000100047&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1405-77432005000100047&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1405-77432005000100047&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Los algoritmos de corte de Gomory para resolver programas lineales en enteros tienen que encontrar una solución entera a un programa lineal obtenido del original al que se le hicieron unos &#8220;cortes.&#8221; La presentación en los textos de dichos algoritmos, generalmente son muy abstractas y difíciles de seguir, máxime que pocos textos presentan ejemplos en todo detalle donde se vea exactamente qué hace cada corte. En este artículo, se muestran varios ejemplos con soluciones detalladas y con una complejidad creciente de problemas, cuyas soluciones deben ser enteras y positivas utilizando matemáticas recreativas (acertijos matemáticos). Los problemas se resuelven mostrando la utilidad de algunas ideas sencillas para obligar a las soluciones a ser enteras. Como esta idea es nueva y funda mental acerca de los algoritmos de Gomory, ya que las demás son las del algoritmo simplex, el artículo sirve para entender mejor los algoritmos de cortes evitando el misterio que genera la excesiva abstracción y la compleja notación de los textos en la materia.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract The cutting algorithms of Gomory for solving linear integer programs find an integer solution to a linear program obtained from the original problem to which some &#8220;cuts&#8221; have been added. The presentations given in the text books that introduce these algorithms are generally abstract and difficult to visualise, of ten because the texts do not pro ide de tailed examples in which the reader can see clearly what each cut does. In this article we use recreational mathematics (math puzzles) and give several examples of increasing complexity to get her with their detailed solutions for problems in which positive integer solutions are required, as means to explaining what is going on with the cuts. The example problems are solved by showing the use fulness of some simple ideas that force the solutions to be integers. Since this is the fundamental new idea of Gomory&#8217;s cutting algorithms, given that the other ideas are those already in use by the simplex algorithm, the article should be useful to help students understand better the cutting algorithms by eliminating the mystery generated by the excessive abstraction and the complex notation of the corresponding text books.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Ecuaciones diofantinas]]></kwd>
<kwd lng="es"><![CDATA[programación lineal entera]]></kwd>
<kwd lng="es"><![CDATA[algoritmos de corte]]></kwd>
<kwd lng="es"><![CDATA[matemáticas recreativas]]></kwd>
<kwd lng="es"><![CDATA[Gomory]]></kwd>
<kwd lng="en"><![CDATA[Diophantine equations]]></kwd>
<kwd lng="en"><![CDATA[integerlinear programming]]></kwd>
<kwd lng="en"><![CDATA[cutting algorithms]]></kwd>
<kwd lng="en"><![CDATA[recreational mathematics]]></kwd>
<kwd lng="en"><![CDATA[Gomory]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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