{"id":969,"date":"2024-12-09T08:00:00","date_gmt":"2024-12-09T07:00:00","guid":{"rendered":"https:\/\/control-advent.com\/?p=969"},"modified":"2025-11-28T19:04:55","modified_gmt":"2025-11-28T18:04:55","slug":"09-o-desafio-da-duende-chevi-bicicletas-pensos-e-equilibrio","status":"publish","type":"post","link":"https:\/\/control-advent.com\/?p=969","title":{"rendered":"09 &#8211; O Desafio da Duende Mercurina: Bicicletas e Pensos M\u00e1gicos"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong><strong><strong>Autora desta quest\u00e3o:<\/strong><\/strong><\/strong> Steffi Knorn, <em>Fachgebiet <em>Regelungstechnik<\/em>, <\/em>Technische Universit\u00e4t Berlin, Alemanha<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sob crescente press\u00e3o devido \u00e0 amea\u00e7a de greve por parte dos duendes, o Pai Natal meteu m\u00e3os \u00e0 obra e recorreu \u00e0 Teoria do Controlo para salvar a sua linha de produ\u00e7\u00e3o no P\u00f3lo Norte.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">O fabrico de presentes est\u00e1 a\u00ed muito atrasado! Por isso, o chefe dos duendes deu a seguinte ordem: &lt;&lt;Arregacem as mangas e m\u00e3os \u00e0 obra!&gt;&gt; &#8212; O que significa que os duendes respons\u00e1veis por cada sec\u00e7\u00e3o devem aumentar a produtividade de forma a alcan\u00e7ar as metas estabelecidas.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A duende Mercurina, respons\u00e1vel pela produ\u00e7\u00e3o de bicicletas, tem como objetivo fabricar 18 bicicletas nos pr\u00f3ximos cinco dias. Sabe que quanto mais arrega\u00e7ar as mangas, mais depressa ela e a sua equipa conseguem trabalhar. Arrega\u00e7ar as mangas at\u00e9 ao n\u00edvel um produz uma bicicleta, at\u00e9 ao n\u00edvel dois produz duas bicicletas, e assim sucessivamente.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">No entanto, arrega\u00e7ar as mangas traz riscos. Com as mangas mais subidas, os bra\u00e7os dos duendes ficam mais expostos a arranh\u00f5es e cortes. Al\u00e9m disso, com o aumento da velocidade e do movimento, os bra\u00e7os t\u00eam maior probabilidade de colidir com objetos, aumentando o risco de les\u00f5es. Ent\u00e3o, isto significa que o n\u00famero de les\u00f5es aumenta quadraticamente com o n\u00edvel de mangas arrega\u00e7adas. Por exemplo, com as mangas no n\u00edvel cinco registam-se cerca de 25 les\u00f5es por dia, enquanto que no n\u00edvel dois se verificam apenas cerca de quatro les\u00f5es.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cada les\u00e3o exige um penso m\u00e1gico, que \u00e9 eficaz mas n\u00e3o reutiliz\u00e1vel e bastante oneroso. Por isso, a Mercurina preocupa-se em minimizar tanto o n\u00famero de les\u00f5es como o n\u00famero de pensos usados.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Qual \u00e9 o melhor plano para a Mercurina alcan\u00e7ar o seu objetivo de produ\u00e7\u00e3o de bicicletas, minimizando as les\u00f5es e poupando assim nos pensos?<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1021\" height=\"1024\" src=\"https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/09-Dec-2024.jpeg\" alt=\"\" class=\"wp-image-422\" style=\"width:auto;height:600px\" srcset=\"https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/09-Dec-2024.jpeg 1021w, https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/09-Dec-2024-300x300.jpeg 300w, https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/09-Dec-2024-150x150.jpeg 150w, https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/09-Dec-2024-768x770.jpeg 768w, https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/09-Dec-2024-24x24.jpeg 24w, https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/09-Dec-2024-36x36.jpeg 36w, https:\/\/control-advent.com\/wp-content\/uploads\/2024\/11\/09-Dec-2024-48x48.jpeg 48w\" sizes=\"auto, (max-width: 1021px) 100vw, 1021px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">a. \ud83d\udeb4\u200d\u2642\ufe0f\ud83d\udcaa\ud83c\udf89 Fazer com que todos os duendes arregacem as mangas at\u00e9 ao n\u00edvel seis e produzam o maior n\u00famero poss\u00edvel de bicicletas. Afinal \u00e9 esse o prop\u00f3sito de arrega\u00e7ar as mangas! Qualquer bicicleta extra poder\u00e1 ser utilizada pelos duendes para se divertirem na oficina no \u00faltimo dia.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b. \ud83d\udee0\ufe0f\ud83c\udfaf\ud83d\ude0c Fazer com que todos os duendes arregacem as mangas at\u00e9 ao n\u00edvel seis e trabalhem at\u00e9 atingir o n\u00famero desejado de bicicletas. Assim que alcan\u00e7arem o objetivo, devem baixar as mangas para o n\u00edvel zero e descansar.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">c. \ud83d\udcc6\ud83e\udd1d\ud83d\udeb2 Fazer com que todos os duendes arregacem as mangas at\u00e9 ao n\u00edvel tr\u00eas durante dois dias e at\u00e9 ao n\u00edvel quatro durante tr\u00eas dias. A ordem dos dias em que as mangas est\u00e3o arrega\u00e7adas at\u00e9 ao n\u00edvel tr\u00eas ou quatro n\u00e3o \u00e9 relevante.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d. \u23f3\ud83d\udcc9\ud83d\udeb4\u200d\u2642\ufe0fFazer com que os duendes arregacem as mangas at\u00e9 ao n\u00edvel quatro durante os primeiros quatro dias e que as baixem para o n\u00edvel dois no \u00faltimo dia.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">e. \ud83d\udd22\u2728\u2696\ufe0f Fazer com que todos os duendes arregacem as mangas at\u00e9 ao n\u00edvel tr\u00eas, pois \u00e9 um meio-termo e parece ser um bom compromisso. Al\u00e9m disso, o tr\u00eas \u00e9 um n\u00famero m\u00e1gico, n\u00e3o \u00e9?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">f. \ud83e\udde5\ud83d\udee1\ufe0f\ud83c\udf43 Fazer com que todos os duendes arregacem as mangas at\u00e9 ao n\u00edvel um para garantir que o n\u00famero de les\u00f5es seja m\u00ednimo.<\/p>\n\n\n<div class=\"yop-poll-container\" data-yop-poll-id=\"14\"><script type=\"application\/json\" data-yop-poll-init>{\"poll\":{\"id\":\"14\",\"name\":\"09-Dec-2024\",\"template\":\"3\",\"template_base\":\"classic\",\"skin_base\":\"red-v1\",\"status\":\"published\",\"meta_data\":{\"style\":{\"poll\":{\"backgroundColor\":\"#b70004\",\"borderSize\":0,\"borderStyle\":\"none\",\"borderColor\":\"#b70004\",\"borderRadius\":0,\"paddingLeftRight\":10,\"paddingTopBottom\":10},\"questions\":{\"paddingLeftRight\":0,\"paddingTopBottom\":10,\"textColor\":\"#ffffff\",\"textSize\":14,\"textWeight\":\"normal\",\"textAlign\":\"center\"},\"answers\":{\"paddingLeftRight\":0,\"paddingTopBottom\":0,\"textColor\":\"#ffffff\",\"textSize\":14,\"textWeight\":\"normal\",\"skin\":\"minimal\",\"colorScheme\":\"black\"},\"buttons\":{\"backgroundColor\":\"#ffffff\",\"borderSize\":1,\"borderStyle\":\"solid\",\"borderColor\":\"#000000\",\"borderRadius\":0,\"paddingLeftRight\":10,\"paddingTopBottom\":5,\"textColor\":\"#000000\",\"textSize\":14,\"textWeight\":\"normal\",\"align\":\"center\"},\"errors\":{\"borderLeftColorForSuccess\":\"#008000\",\"borderLeftColorForError\":\"#ff0000\",\"borderLeftSize\":10,\"paddingTopBottom\":0,\"textColor\":\"#000000\",\"textSize\":14,\"textWeight\":\"normal\"},\"captcha\":[],\"custom\":{\"css\":\"\"}},\"options\":{\"poll\":{\"voteButtonLabel\":\"&gt;&gt;&gt;\",\"showResultsLink\":\"no\",\"resultsLabelText\":\"Results\",\"showTotalVotes\":\"no\",\"showTotalAnswers\":\"no\",\"startDateOption\":\"now\",\"startDateCustom\":\"\",\"endDateOption\":\"never\",\"endDateCustom\":\"\",\"redirectAfterVote\":\"no\",\"redirectUrl\":\"\",\"redirectAfter\":\"\",\"pageLink\":\"\",\"useCaptcha\":\"no\",\"enableGdpr\":\"no\",\"gdprSolution\":\"ask_consent\",\"gdprConsentText\":\"\",\"loadWithAjax\":\"no\",\"notificationMessageLocation\":\"top\"},\"results\":{\"showResultsMoment\":[\"never\"],\"customDateResults\":\"\",\"showResultsTo\":[],\"resultsDetails\":[\"percentages\"],\"backToVoteOption\":\"no\",\"backToVoteCaption\":\"Back to vote\",\"sortResults\":\"as-defined\",\"sortResultsRule\":\"asc\",\"displayResultsAs\":\"bar\"},\"access\":{\"votePermissions\":[\"wordpress\"]}}}},\"elements\":[{\"id\":\"14\",\"poll_id\":\"14\",\"etext\":\"Choose an option:\",\"etype\":\"question-text\",\"status\":\"active\",\"sorder\":\"1\",\"meta_data\":{\"allowOtherAnswers\":\"no\",\"otherAnswersLabel\":\"Other\",\"addOtherAnswers\":\"no\",\"displayOtherAnswersInResults\":\"no\",\"resultsColorForOtherAnswers\":\"#000000\",\"allowMultipleAnswers\":\"no\",\"multipleAnswersMinim\":\"1\",\"multipleAnswersMaxim\":\"1\",\"answersDisplay\":\"horizontal\",\"answersColumns\":\"\",\"answersSort\":\"as-defined\"},\"subelements\":[{\"id\":\"88\",\"poll_id\":\"14\",\"element_id\":\"14\",\"stext\":\"a\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"1\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}},{\"id\":\"89\",\"poll_id\":\"14\",\"element_id\":\"14\",\"stext\":\"b\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"2\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}},{\"id\":\"90\",\"poll_id\":\"14\",\"element_id\":\"14\",\"stext\":\"c\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"3\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}},{\"id\":\"127\",\"poll_id\":\"14\",\"element_id\":\"14\",\"stext\":\"d\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"4\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}},{\"id\":\"128\",\"poll_id\":\"14\",\"element_id\":\"14\",\"stext\":\"e\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"5\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}},{\"id\":\"129\",\"poll_id\":\"14\",\"element_id\":\"14\",\"stext\":\"f\",\"stype\":\"text\",\"status\":\"active\",\"sorder\":\"6\",\"meta_data\":{\"makeDefault\":\"0\",\"makeLink\":\"0\",\"link\":\"\",\"resultsColor\":\"#000000\"}}]}],\"messages\":{\"captcha\":{\"accessibility-alt\":\"Sound icon\",\"accessibility-title\":\"Accessibility option: listen to a question and answer it!\",\"accessibility-description\":\"Type below the [STRONG]answer[\\\/STRONG] to what you hear. 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