{"id":457,"date":"2018-11-24T09:13:43","date_gmt":"2018-11-24T08:13:43","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=457"},"modified":"2024-02-11T10:07:59","modified_gmt":"2024-02-11T09:07:59","slug":"how-to-get-answers-of-a-2-by-2-matrix-linear-programming-maximization-problem-without-artificial-variables-using-nickzom-calculator","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2018\/11\/24\/how-to-get-answers-of-a-2-by-2-matrix-linear-programming-maximization-problem-without-artificial-variables-using-nickzom-calculator\/","title":{"rendered":"How to Get Answers of a 2 By 2 Matrix Linear Programming Maximization Problem Without Artificial Variables Using Nickzom Calculator"},"content":{"rendered":"<p>Navigating linear programming maximization problems involving 2 by 2 matrices without artificial variables poses a challenge for many. However, understanding the underlying principles and employing strategic techniques can simplify the process significantly. Many students and professionals can do with help from a specialized calculator that helps them solve Matrix Linear Programming Maximization Probelms as well as showing them the workings. This is where Nickzom calculator comes in.<\/p>\n<p>However, before we get to that, let&#8217;s explore efficient methods to obtain solutions and optimize decision-making in such scenarios.<\/p>\n<p>According to <a href=\"https:\/\/www.google.com.ng\/search?q=linear+programming&amp;oq=linear+programming&amp;aqs=chrome..69i57j69i61j69i60j69i61j0l2.42157j0j7&amp;sourceid=chrome&amp;ie=UTF-8\">Google Dictionary<\/a>, <strong>Linear Programming<\/strong> is a mathematical technique for maximizing or minimizing a linear function of several variables, such as output or cost.<\/p>\n<p>On the other hand, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Mathematical_optimization\">Wikipedia<\/a> describes as <strong>L<\/strong><b>inear programming<\/b>\u00a0(<b>LP<\/b>, also called\u00a0<b>linear optimization<\/b>) a method to achieve the best outcome (such as maximum profit or lowest cost) in a <a title=\"Mathematical model\" href=\"https:\/\/en.wikipedia.org\/wiki\/Mathematical_model\">mathematical model<\/a>\u00a0whose requirements are represented by\u00a0<a title=\"Linear function\" href=\"https:\/\/en.wikipedia.org\/wiki\/Linear_function#As_a_polynomial_function\">linear relationships<\/a>. Linear programming is a special case of mathematical programming (also known as\u00a0<a title=\"Mathematical optimization\" href=\"https:\/\/en.wikipedia.org\/wiki\/Mathematical_optimization\">mathematical optimization<\/a>).<\/p>\n<h3>Solving Linear Programming Maximization with Nickzom Calculator<\/h3>\n<p>You might be wondering how possible is it for there to be a calculator that can really solve linear programming calculations and show the workings at the same time. <strong>Nickzom Calculator<\/strong> does that for you at the very best of all capabilities.<\/p>\n<p>Nickzom Calculator can not only solve a 2 by 2 matrix linear programming problem but can also solve for an m by n matrix problem. At the moment, Nickzom Calculator can handle:<\/p>\n<ul>\n<li>Maximization Without Artificial Variable(s)<\/li>\n<li>Minimization Without Artificial Variable(s)<\/li>\n<\/ul>\n<p>Computations of Linear Programming with artificial variables is on the way and I do promise to inform you once it is integrated into the calculator encyclopedia via this blog.<\/p>\n<p>Nickzom Calculator makes use of <strong>simplex method<\/strong> to compute the result for linear programming problems. There is an iterative computation of steps to obtain the final result which is when\u00a0there is no further negative entry in the index\/third\/<b>P<\/b>\u00a0row of which a basic solution emerges for x and y variables with all the other variables equal to <strong>0<\/strong>. At this point, the <strong>optimal solution<\/strong> and <strong>optimal value<\/strong> is given.<\/p>\n<h3>Steps in Iterative Simplex Method<\/h3>\n<p><!--more--><\/p>\n<p>The various steps used in the <strong>iterative<\/strong> simplex method are outlined accordingly:<\/p>\n<ul>\n<li>Obtain the key column which is the column containing the most negative entry in the index row.<\/li>\n<li>Obtain the key row by dividing the value in the b column by the entry in the key column, of which the smallest positive ratio determines the key row.<\/li>\n<li>Divide all entries in the key row by the\u00a0<b>pivot<\/b>\u00a0to reduce the pivot to\u00a0<b>unity<\/b>\u00a0(that is 1).<\/li>\n<li>Make use of the main row to work on the remaining rows of the table to reduce the other entries in the key column to zero.<\/li>\n<li>If there is a presence of negative entry in the index\/third\/P row. <strong>Repeat Steps<\/strong> from Beginning.<\/li>\n<\/ul>\n<p>The moment you have been waiting for, how can Nickzom Calculator solve this operation. First and Foremost, access Nickzom Calculator &#8211; <strong>The Calculator Encyclopedia\u00a0<\/strong>via any of these means:<\/p>\n<p>Web \u2013\u00a0<a href=\"https:\/\/www.nickzom.org\/calculator-plus\">https:\/\/www.nickzom.org\/calculator-plus<\/a><\/p>\n<p>Android (Paid) \u2013\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator\">https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator<\/a><\/p>\n<p>Apple (Paid) \u2013\u00a0<a href=\"https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8\">https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8<\/a><\/p>\n<p>Proceed to <strong>Calculator Map<\/strong> under the Engineering Section<\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-458 size-large\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-219-1024x576.png\" alt=\"How to Get Answers of a 2 By 2 Matrix Linear Programming Maximization Problem Without Artificial Variables Using Nickzom Calculator\" width=\"800\" height=\"450\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-219-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-219-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-219-768x432.png 768w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-219.png 1366w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>Click on <strong>Linear Programming<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-459 size-large\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-216-1024x576.png\" alt=\"How to Get Answers of a 2 By 2 Matrix Linear Programming Maximization Problem Without Artificial Variables Using Nickzom Calculator\" width=\"800\" height=\"450\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-216-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-216-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-216-768x432.png 768w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-216.png 1366w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>Click on <strong>Maximization Without Artificial Variables<\/strong><\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-460 size-large\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-217-1024x576.png\" alt=\"How to Get Answers of a 2 By 2 Matrix Linear Programming Maximization Problem Without Artificial Variables Using Nickzom Calculator\" width=\"800\" height=\"450\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-217-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-217-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-217-768x432.png 768w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-217.png 1366w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>Nickzom Calculator computes for two means of maximization without artificial variable(s), which are:<\/p>\n<ul>\n<li>Simplex with Two <strong>Problem Variables<\/strong> | Two <strong>Inequalities<\/strong><\/li>\n<li>Simplex with N <strong>Problem Variables<\/strong> | M <strong>Inequalities<\/strong><\/li>\n<\/ul>\n<p>Since the purpose of this post is a 2 by 2 matrix, click on simplex with two problem variables and two inequalities.<\/p>\n<p><img decoding=\"async\" class=\"alignnone wp-image-461 size-large\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-218-1024x576.png\" alt=\"How to Get Answers of a 2 By 2 Matrix Linear Programming Maximization Problem Without Artificial Variables Using Nickzom Calculator\" width=\"800\" height=\"450\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-218-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-218-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-218-768x432.png 768w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-218.png 1366w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>Now, enter your values and coefficients accurately just like the image below<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-large wp-image-462\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-220-1024x576.png\" alt=\"\" width=\"660\" height=\"371\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-220-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-220-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-220-768x432.png 768w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/Screenshot-220.png 1366w\" sizes=\"(max-width: 660px) 100vw, 660px\" \/><\/p>\n<p>All you have to do now, my loving friend is just click on the <strong>Calculate<\/strong> and Nickzom Calculator works its magic in less than a second and displays for you the result with the complete workings and tutorials. For the purpose of this post, I would display the result in the form of a <strong>video<\/strong>. Watch and Enjoy!<\/p>\n<div style=\"width: 1200px;\" class=\"wp-video\"><video class=\"wp-video-shortcode\" id=\"video-457-1\" width=\"1200\" height=\"646\" preload=\"metadata\" controls=\"controls\"><source type=\"video\/mp4\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/2018-11-24-at-09-18-02.mp4?_=1\" \/><a href=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/2018-11-24-at-09-18-02.mp4\">https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2018\/11\/2018-11-24-at-09-18-02.mp4<\/a><\/video><\/div>\n","protected":false},"excerpt":{"rendered":"Navigating linear programming maximization problems involving 2 by 2 matrices without artificial variables poses a challenge for many.&hellip;","protected":false},"author":1,"featured_media":12205,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_opengraph-title":"","_yoast_wpseo_opengraph-description":"","_yoast_wpseo_twitter-title":"","_yoast_wpseo_twitter-description":"","_lmt_disableupdate":"","_lmt_disable":"","_sitemap_exclude":false,"_sitemap_priority":"","_sitemap_frequency":"","_yoast_wpseo_focuskw_text_input":"","csco_display_header_overlay":false,"csco_singular_sidebar":"","csco_page_header_type":"","footnotes":"","_members_access_role":[],"_members_access_error":""},"categories":[47,4],"tags":[186,54,84,60,183,187,181,56,93,185,87,184,182],"class_list":["post-457","post","type-post","status-publish","format-standard","has-post-thumbnail","category-engineering","category-mathematics","tag-artificial-variables","tag-calculator","tag-calculator-encyclopedia","tag-engineering","tag-inequalities","tag-linear-optimization","tag-linear-programming","tag-mathematics","tag-matrix","tag-maximization","tag-nickzom-calculator","tag-optimization","tag-problem-variables","cs-entry"],"yoast_head":"<!-- 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