{"id":396,"date":"2023-01-20T04:06:52","date_gmt":"2023-01-20T04:06:52","guid":{"rendered":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/?page_id=396"},"modified":"2024-11-12T17:26:46","modified_gmt":"2024-11-12T17:26:46","slug":"learning-activity-for-lagrange-multiplier-optimization","status":"publish","type":"page","link":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/learning-activity-for-lagrange-multiplier-optimization\/","title":{"rendered":"Learning Activity for Lagrange Multiplier Optimization"},"content":{"rendered":"<p><a href=\"http:\/\/sites.monroecc.edu\/multivariablecalculus\/files\/2023\/01\/20221117_001718-scaled.jpg\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-381\" src=\"http:\/\/sites.monroecc.edu\/multivariablecalculus\/files\/2023\/01\/20221117_001718-300x300.jpg\" alt=\"Thermoformed mountainous surface with circular path drawn on it\" width=\"400\" height=\"400\" srcset=\"https:\/\/sites.monroecc.edu\/multivariablecalculus\/files\/2023\/01\/20221117_001718-300x300.jpg 300w, https:\/\/sites.monroecc.edu\/multivariablecalculus\/files\/2023\/01\/20221117_001718-1024x1024.jpg 1024w, https:\/\/sites.monroecc.edu\/multivariablecalculus\/files\/2023\/01\/20221117_001718-150x150.jpg 150w, https:\/\/sites.monroecc.edu\/multivariablecalculus\/files\/2023\/01\/20221117_001718-768x768.jpg 768w, https:\/\/sites.monroecc.edu\/multivariablecalculus\/files\/2023\/01\/20221117_001718-1536x1536.jpg 1536w, https:\/\/sites.monroecc.edu\/multivariablecalculus\/files\/2023\/01\/20221117_001718-2048x2048.jpg 2048w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>This activity is designed to help students gain 3D visual intuition for the meaning of the Lagrange Multiplier approach to constrained optimization.\u00a0 It is intended as an introduction to this topic to guide students through the discovery of the relationships involved.<\/p>\n<p>We have two different versions of this activity:<\/p>\n<ul>\n\t<li>An instructor-led discussion using a script in CalcPlot3D (Shelby&#8217;s):\n\n<ul>\n\t<li>PDF for Shelby&#8217;s version: <strong><a href=\"https:\/\/sites.monroecc.edu\/multivariablecalculus\/learning-activity-for-lagrange-multiplier-optimization\/lagrange_multipliers_activity_using_script\/\" target=\"_blank\" rel=\"noreferrer noopener\">Lagrange_Multipliers_Activity_Using_Script<\/a><\/strong><\/li>\n\t<li>Word file for Shelby&#8217;s version:\u00a0 <a href=\"https:\/\/paulseeburger.sfo2.digitaloceanspaces.com\/CalcPlot3D\/activities\/Lagrange_Multipliers_Activity_Using_Script.docx\"><strong>Lagrange_Multipliers_Activity_Using_Script.docx<\/strong><\/a><\/li>\n\t<li>Instructor&#8217;s guide: <strong><a href=\"https:\/\/sites.monroecc.edu\/multivariablecalculus\/learning-activity-for-lagrange-multiplier-optimization\/lagrange_mulitplier_activity_with_script_instructor_notes\/\" target=\"_blank\" rel=\"noreferrer noopener\">Lagrange_Mulitplier_Activity_with_Script Instructor Notes<\/a><\/strong><\/li>\n<\/ul>\n<\/li>\n\t<li>An instructor-guided small group activity (Paul&#8217;s):\n\n<ul>\n\t<li>PDF for Paul&#8217;s version: <strong><a href=\"https:\/\/sites.monroecc.edu\/multivariablecalculus\/learning-activity-for-lagrange-multiplier-optimization\/212la-lagrangemultipliers-v3f24\/\" target=\"_blank\" rel=\"noreferrer noopener\">212LA-LagrangeMultipliers-v3F24<\/a><\/strong><\/li>\n\t<li>Word file for Paul&#8217;s version:\u00a0 <a href=\"https:\/\/paulseeburger.sfo2.digitaloceanspaces.com\/CalcPlot3D\/activities\/212LA-LagrangeMultipliers-v3F24.docx\"><strong>212LA-LagrangeMultipliers-v3F24.docx<\/strong><\/a><\/li>\n\t<li>Contour plot page for this activity (PDF): <strong><a href=\"https:\/\/sites.monroecc.edu\/multivariablecalculus\/learning-activity-for-lagrange-multiplier-optimization\/212la-lagrangeactivity-basepage-v5\/\" target=\"_blank\" rel=\"noreferrer noopener\">212LA-LagrangeActivity-basepage-v5<\/a><\/strong><\/li>\n\t<li>Word file with this contour plot page:\u00a0 <a href=\"https:\/\/paulseeburger.sfo2.digitaloceanspaces.com\/CalcPlot3D\/activities\/212LA-LagrangeActivity-basepage-v5.docx\"><strong>212LA-LagrangeActivity-basepage-v5.docx<\/strong><\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>For both versions of this activity we used a 3D-printed form along with a thermoformer to create the plastic surfaces.<\/p>\n<p>Here is the STL file for this mold: <strong><a href=\"https:\/\/sites.monroecc.edu\/multivariablecalculus\/learning-activity-for-lagrange-multiplier-optimization\/surface1_mold_improved-stl\/\">Surface1_Mold_improved-STL<\/a><\/strong><br>\nNote that you will still need to set up the 3D print to optimize it for thermoforming.\u00a0 As described below, I&#8217;ve found 13 walls, no floor, and a 20% gyroid infill seems to work well.<\/p>\n<p>Here is the Cura .3mf file for the surface whose contour plot is shown in the activity.\u00a0 It&#8217;s set up for an Ultimaker S5 3D printer, but should work with an Ultimaker S3 as well.\u00a0 It is configured to use 13 walls, no floor and gyroid infill at 20%.\u00a0 These settings have worked well to keep the mold from deforming during the thermoforming process.<\/p>\n<p><strong><a href=\"https:\/\/sites.monroecc.edu\/multivariablecalculus\/learning-activity-for-lagrange-multiplier-optimization\/whitemountain-mold-3mf-cura-file\/\">White Mountain Mold &#8211; Cura .3mf file for the surface mold in a .zip file<\/a><\/strong><\/p>\n<p>Below you can see the <span class=\"s1\">Vaquform DT2 thermoformer that I used for this purpose in my office.<\/span><\/p>\n\n<figure id=\"attachment_397\" aria-describedby=\"caption-attachment-397\" style=\"width: 749px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/sites.monroecc.edu\/multivariablecalculus\/files\/2023\/01\/20221103_164026_HDR-scaled.jpg\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-397\" src=\"http:\/\/sites.monroecc.edu\/multivariablecalculus\/files\/2023\/01\/20221103_164026_HDR-1024x768.jpg\" alt=\"Image of a thermoformer\" width=\"749\" height=\"562\" srcset=\"https:\/\/sites.monroecc.edu\/multivariablecalculus\/files\/2023\/01\/20221103_164026_HDR-1024x768.jpg 1024w, https:\/\/sites.monroecc.edu\/multivariablecalculus\/files\/2023\/01\/20221103_164026_HDR-300x225.jpg 300w, https:\/\/sites.monroecc.edu\/multivariablecalculus\/files\/2023\/01\/20221103_164026_HDR-768x576.jpg 768w, https:\/\/sites.monroecc.edu\/multivariablecalculus\/files\/2023\/01\/20221103_164026_HDR-1536x1152.jpg 1536w, https:\/\/sites.monroecc.edu\/multivariablecalculus\/files\/2023\/01\/20221103_164026_HDR-2048x1536.jpg 2048w\" sizes=\"auto, (max-width: 749px) 100vw, 749px\" \/><\/a><figcaption id=\"caption-attachment-397\" class=\"wp-caption-text\">Image of the <span class=\"s1\">Vaquform DT2<\/span> thermoformer<\/figcaption><\/figure>","protected":false},"excerpt":{"rendered":"<p>This activity is designed to help students gain 3D visual intuition for the meaning of the Lagrange Multiplier approach to constrained optimization.\u00a0 It is intended as an introduction to this topic to guide students through the discovery of the relationships involved. We have two different versions of this activity: An instructor-led discussion using a script [&#8230;]<\/p>\n","protected":false},"author":654,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-396","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/wp-json\/wp\/v2\/pages\/396","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/wp-json\/wp\/v2\/users\/654"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/wp-json\/wp\/v2\/comments?post=396"}],"version-history":[{"count":23,"href":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/wp-json\/wp\/v2\/pages\/396\/revisions"}],"predecessor-version":[{"id":617,"href":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/wp-json\/wp\/v2\/pages\/396\/revisions\/617"}],"wp:attachment":[{"href":"https:\/\/sites.monroecc.edu\/multivariablecalculus\/wp-json\/wp\/v2\/media?parent=396"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}