{"id":24081,"date":"2026-08-06T07:33:41","date_gmt":"2026-08-06T07:33:41","guid":{"rendered":"https:\/\/www.vedprep.com\/exams\/?p=24081"},"modified":"2026-08-06T07:33:41","modified_gmt":"2026-08-06T07:33:41","slug":"simplex-method-3","status":"publish","type":"post","link":"https:\/\/www.vedprep.com\/exams\/uppsc\/simplex-method-3\/","title":{"rendered":"Simplex Method 2025: Ultimate Guide for UPPSC Assistant"},"content":{"rendered":"<h2>Simplex Method: The Definitive Algorithm for Linear Programming<\/h2>\n<p>The <strong>Simplex Method<\/strong> is the cornerstone algorithm for solving linear programming problems (LPP). This iterative technique systematically evaluates feasible solutions to identify the optimal outcome, making it indispensable for UPPSC Assistant Professor aspirants preparing for CSIR NET, IIT JAM, and GATE exams. Understanding the <strong>Simplex Method<\/strong> equips candidates with the tools to tackle complex optimization challenges in operations research and beyond.<\/p>\n<p>At its core, the <strong>Simplex Method<\/strong> transforms a linear programming problem into a series of algebraic operations. By navigating the vertices of the feasible region, it efficiently converges to the optimal solution. This guide explores the <strong>Simplex Method<\/strong> in depth, from foundational concepts to advanced applications, ensuring comprehensive preparation for competitive exams.<\/p>\n<h2>Why the Simplex Method Matters for UPPSC Assistant Professor Exams<\/h2>\n<p>The <strong>Simplex Method<\/strong> is a critical topic in the syllabi of several competitive exams, including:<\/p>\n<ul>\n<li><strong>CSIR NET:<\/strong> Covered under Unit 4 (Linear Algebra, Calculus, and Probability, Statistics)<\/li>\n<li><strong>IIT JAM:<\/strong> Included in Mathematics, Physics, and Chemistry papers<\/li>\n<li><strong>UPPSC Assistant Professor:<\/strong> Essential for Mathematics, Statistics, and Computer Science streams<\/li>\n<\/ul>\n<p>Mastering the <strong>Simplex Method<\/strong> not only boosts exam performance but also enhances problem-solving skills for real-world applications. Standard textbooks like <em>\u201cIntroduction to Operations Research\u201d by Hillier and Lieberman<\/em> and <em>\u201cLinear Programming and Network Flows\u201d by Bazaraa et al.<\/em> provide in-depth coverage of this algorithm.<\/p>\n<h2>Simplex Method Step-by-Step: From Theory to Practice<\/h2>\n<p>The <strong>Simplex Method<\/strong> follows a structured approach to solve linear programming problems. Below is a detailed breakdown of each step, ensuring clarity and precision for UPPSC Assistant Professor candidates.<\/p>\n<h3>Step 1: Formulate the Linear Programming Problem<\/h3>\n<p>Begin by defining the objective function and constraints. The objective function is a linear equation representing the goal (e.g., maximize profit or minimize cost), while constraints are linear inequalities or equations that limit the solution space. For example, consider the problem:<\/p>\n<p>Maximize <em>Z = 3x + 4y<\/em><br \/>Subject to:<br \/>2x + 3y \u2264 12<br \/>x \u2265 0, y \u2265 0<\/p>\n<p>This formulation sets the stage for applying the <strong>Simplex Method<\/strong>.<\/p>\n<h3>Step 2: Convert to Standard Form<\/h3>\n<p>The <strong>Simplex Method<\/strong> requires the problem to be in standard form, where:<\/p>\n<ul>\n<li>The objective function is maximized<\/li>\n<li>All constraints are equations with non-negative right-hand sides<\/li>\n<li>All variables are non-negative<\/li>\n<\/ul>\n<p>To achieve this, introduce <em>slack variables<\/em> to convert inequalities into equations. For the example above, the constraint <em>2x + 3y \u2264 12<\/em> becomes <em>2x + 3y + s = 12<\/em>, where <em>s<\/em> is a slack variable.<\/p>\n<h3>Step 3: Construct the Initial Simplex Tableau<\/h3>\n<p>The simplex tableau is a tabular representation of the linear programming problem. It includes the objective function and constraints, with columns for each variable and a right-hand side (RHS) column. For the example, the initial tableau is:<\/p>\n<table>\n<tr>\n<th>| x | y | s | RHS<\/th>\n<\/tr>\n<tr>\n<th>Z | -3 | -4 | 0 | 0<\/th>\n<\/tr>\n<tr>\n<th>s | 2 | 3 | 1 | 12<\/th>\n<\/tr>\n<\/table>\n<p>The <strong>Simplex Method<\/strong> uses this tableau to iteratively improve the solution.<\/p>\n<h3>Step 4: Identify the Pivot Element<\/h3>\n<p>The pivot element is selected based on the most negative coefficient in the objective function row (Z-row). In the example, the most negative value is -4, corresponding to the <em>y<\/em> column. The pivot row is determined using the minimum ratio test, which compares the RHS values to the pivot column values. Here, the ratio for the <em>s<\/em>-row is <em>12\/3 = 4<\/em>, making <em>3<\/em> the pivot element.<\/p>\n<h3>Step 5: Perform Row Operations to Update the Tableau<\/h3>\n<p>Using the pivot element, perform row operations to create a new tableau. The goal is to transform the pivot column into a unit column (all zeros except for the pivot element, which becomes 1). For the example, the updated tableau is:<\/p>\n<table>\n<tr>\n<th>| x | y | s | RHS<\/th>\n<\/tr>\n<tr>\n<th>Z | -3 | 0 | 4\/3 | 16<\/th>\n<\/tr>\n<tr>\n<th>y | 2\/3 | 1 | 1\/3 | 4<\/th>\n<\/tr>\n<\/table>\n<p>The <strong>Simplex Method<\/strong> continues this process until no negative coefficients remain in the Z-row, indicating an optimal solution.<\/p>\n<h3>Step 6: Interpret the Optimal Solution<\/h3>\n<p>In the final tableau, the optimal solution is read directly from the RHS column. For the example, the solution is <em>x = 0<\/em> and <em>y = 4<\/em>, yielding a maximum <em>Z = 16<\/em>. This demonstrates the power of the <strong>Simplex Method<\/strong> in solving linear programming problems efficiently.<\/p>\n<h2>Simplex Method Worked Example: Solving a Classic LPP<\/h2>\n<p>To solidify understanding, let\u2019s solve a classic linear programming problem using the <strong>Simplex Method<\/strong>. Consider the following:<\/p>\n<p>Maximize <em>Z = 5x + 6y<\/em><br \/>Subject to:<br \/>2x + 3y \u2264 18<br \/>4x + 2y \u2264 20<br \/>x \u2265 0, y \u2265 0<\/p>\n<p>Follow these steps to apply the <strong>Simplex Method<\/strong>:<\/p>\n<h3>1. Convert to Standard Form<\/h3>\n<p>Introduce slack variables <em>s\u2081<\/em> and <em>s\u2082<\/em> to convert the inequalities into equations:<\/p>\n<p>2x + 3y + s\u2081 = 18<br \/>4x + 2y + s\u2082 = 20<\/p>\n<h3>2. Construct the Initial Tableau<\/h3>\n<table>\n<tr>\n<th>| x | y | s\u2081 | s\u2082 | RHS<\/th>\n<\/tr>\n<tr>\n<th>Z | -5 | -6 | 0 | 0 | 0<\/th>\n<\/tr>\n<tr>\n<th>s\u2081 | 2 | 3 | 1 | 0 | 18<\/th>\n<\/tr>\n<tr>\n<th>s\u2082 | 4 | 2 | 0 | 1 | 20<\/th>\n<\/tr>\n<\/table>\n<h3>3. Identify the Pivot Element<\/h3>\n<p>The most negative coefficient in the Z-row is -6, corresponding to the <em>y<\/em> column. The minimum ratio test yields:<\/p>\n<ul>\n<li>For <em>s\u2081<\/em>: 18\/3 = 6<\/li>\n<li>For <em>s\u2082<\/em>: 20\/2 = 10<\/li>\n<\/ul>\n<p>The pivot element is <em>3<\/em> (row <em>s\u2081<\/em>, column <em>y<\/em>).<\/p>\n<h3>4. Update the Tableau<\/h3>\n<p>Perform row operations to create a new tableau:<\/p>\n<table>\n<tr>\n<th>| x | y | s\u2081 | s\u2082 | RHS<\/th>\n<\/tr>\n<tr>\n<th>Z | -1 | 0 | 2 | 0 | 36<\/th>\n<\/tr>\n<tr>\n<th>y | 2\/3 | 1 | 1\/3 | 0 | 6<\/th>\n<\/tr>\n<tr>\n<th>s\u2082 | 8\/3 | 0 | -2\/3 | 1 | 8<\/th>\n<\/tr>\n<\/table>\n<h3>5. Repeat Until Optimality<\/h3>\n<p>The most negative coefficient in the Z-row is now -1, corresponding to the <em>x<\/em> column. The minimum ratio test yields:<\/p>\n<ul>\n<li>For <em>y<\/em>: 6\/(2\/3) = 9<\/li>\n<li>For <em>s\u2082<\/em>: 8\/(8\/3) = 3<\/li>\n<\/ul>\n<p>The pivot element is <em>8\/3<\/em> (row <em>s\u2082<\/em>, column <em>x<\/em>). Update the tableau again:<\/p>\n<table>\n<tr>\n<th>| x | y | s\u2081 | s\u2082 | RHS<\/th>\n<\/tr>\n<tr>\n<th>Z | 0 | 0 | 5\/4 | 3\/8 | 39<\/th>\n<\/tr>\n<tr>\n<th>y | 0 | 1 | 1\/2 | -1\/4 | 4<\/th>\n<\/tr>\n<tr>\n<th>x | 1 | 0 | -1\/4 | 3\/8 | 3<\/th>\n<\/tr>\n<\/table>\n<p>Since no negative coefficients remain in the Z-row, the optimal solution is <em>x = 3<\/em> and <em>y = 4<\/em>, with a maximum <em>Z = 39<\/em>. This example illustrates the effectiveness of the <strong>Simplex Method<\/strong> in solving LPPs.<\/p>\n<h2>Common Misconceptions About the Simplex Method Debunked<\/h2>\n<p>Despite its widespread use, the <strong>Simplex Method<\/strong> is often misunderstood. Here are some common misconceptions and clarifications:<\/p>\n<ul>\n<li><strong>Misconception 1:<\/strong> The <strong>Simplex Method<\/strong> is overly complex.<br \/><em>Reality:<\/em> While the algorithm involves multiple steps, it is a systematic and logical process. With practice, candidates can master the <strong>Simplex Method<\/strong> and apply it confidently.<\/li>\n<li><strong>Misconception 2:<\/strong> The <strong>Simplex Method<\/strong> is limited to small problems.<br \/><em>Reality:<\/em> The <strong>Simplex Method<\/strong> is scalable and can handle large-scale linear programming problems, making it valuable for real-world applications in economics, engineering, and computer science.<\/li>\n<li><strong>Misconception 3:<\/strong> The <strong>Simplex Method<\/strong> always finds the optimal solution.<br \/><em>Reality:<\/em> The <strong>Simplex Method<\/strong> guarantees an optimal solution only if the problem is feasible and bounded. Degeneracy or unboundedness can complicate the process, but advanced techniques can address these issues.<\/li>\n<\/ul>\n<p>Understanding these nuances ensures a robust grasp of the <strong>Simplex Method<\/strong> for UPPSC Assistant Professor exams.<\/p>\n<h2>Real-World Applications of the Simplex Method<\/h2>\n<p>The <strong>Simplex Method<\/strong> is not just an academic concept; it has practical applications across various industries. Here are some key areas where the <strong>Simplex Method<\/strong> is applied:<\/p>\n<h3>1. Economics and Resource Allocation<\/h3>\n<p>Economists use the <strong>Simplex Method<\/strong> to optimize resource allocation, ensuring efficient use of labor, capital, and raw materials. For example, a company can maximize profit by determining the optimal mix of products to manufacture, given resource constraints.<\/p>\n<h3>2. Production Planning<\/h3>\n<p>Manufacturers leverage the <strong>Simplex Method<\/strong> to plan production schedules. By formulating the problem as an LPP, they can minimize costs while meeting demand and resource limitations. This application is crucial for industries like automotive, pharmaceuticals, and consumer goods.<\/p>\n<h3>3. Computer Science and Scheduling<\/h3>\n<p>In computer science, the <strong>Simplex Method<\/strong> is used to solve scheduling problems. For instance, it can optimize CPU time allocation for multiple tasks, ensuring efficient execution and resource utilization. This is particularly valuable in cloud computing and distributed systems.<\/p>\n<h3>4. Logistics and Transportation<\/h3>\n<p>The <strong>Simplex Method<\/strong> helps logistics companies optimize routes and reduce transportation costs. By modeling the problem as an LPP, they can determine the most efficient way to deliver goods while minimizing fuel consumption and travel time.<\/p>\n<p>These applications highlight the versatility of the <strong>Simplex Method<\/strong> in solving complex optimization problems across diverse fields.<\/p>\n<h2>VedPrep\u2019s Proven Study Strategy for Mastering the Simplex Method<\/h2>\n<p>Preparing for the <strong>Simplex Method<\/strong> requires a structured approach. Here\u2019s a step-by-step strategy to master this topic for UPPSC Assistant Professor exams:<\/p>\n<h3>1. Build a Strong Foundation<\/h3>\n<p>Start by understanding the basics of linear programming and the <strong>Simplex Method<\/strong>. Key concepts include:<\/p>\n<ul>\n<li>Objective function and constraints<\/li>\n<li>Feasible region and basic feasible solutions<\/li>\n<li>Simplex tableau and pivot operations<\/li>\n<\/ul>\n<p>Refer to standard textbooks and online resources, such as <a href=\"https:\/\/www.vedprep.com\/\">VedPrep<\/a>, for comprehensive coverage of these topics.<\/p>\n<h3>2. Practice with Worked Examples<\/h3>\n<p>Work through solved examples to grasp the <strong>Simplex Method<\/strong> step-by-step. Start with simple problems and gradually move to complex ones. This hands-on practice reinforces theoretical knowledge and builds confidence.<\/p>\n<h3>3. Solve Past Year Papers<\/h3>\n<p>Analyze past year papers from CSIR NET, IIT JAM, and UPPSC Assistant Professor exams to identify frequently tested subtopics. Focus on:<\/p>\n<ul>\n<li>Standard form conversion<\/li>\n<li>Simplex tableau construction<\/li>\n<li>Interpretation of results<\/li>\n<\/ul>\n<p>This targeted practice ensures familiarity with exam patterns and question types.<\/p>\n<h3>4. Utilize Online Resources<\/h3>\n<p>Leverage free video lectures and tutorials to supplement learning. For example, <a href=\"https:\/\/www.youtube.com\/watch?v=4PdIfAAHtcg\" target=\"_blank\" rel=\"nofollow noopener\">this VedPrep lecture on the Simplex Method<\/a> provides a visual and interactive way to understand the algorithm. Online platforms like <a href=\"https:\/\/www.vedprep.com\/\">VedPrep<\/a> offer expert guidance and study materials tailored for competitive exams.<\/p>\n<h3>5. Time Management and Mock Tests<\/h3>\n<p>Simulate exam conditions by practicing under timed constraints. This helps improve speed and accuracy, ensuring candidates can solve <strong>Simplex Method<\/strong> problems efficiently during the actual exam.<\/p>\n<h2>Advanced Tips for Solving Simplex Method Problems<\/h2>\n<p>To excel in solving <strong>Simplex Method<\/strong> problems, adopt these advanced strategies:<\/p>\n<h3>1. Verify Each Step<\/h3>\n<p>Double-check calculations at every stage of the <strong>Simplex Method<\/strong>. Errors in the tableau or pivot selection can lead to incorrect solutions. Meticulous verification ensures accuracy and builds confidence.<\/p>\n<h3>2. Handle Degeneracy with Care<\/h3>\n<p>Degeneracy occurs when a basic variable takes a zero value, potentially causing cycling. Use techniques like Bland\u2019s rule or lexicographic ordering to address this issue and ensure the <strong>Simplex Method<\/strong> converges to the optimal solution.<\/p>\n<h3>3. Explore Duality<\/h3>\n<p>Understand the relationship between the primal and dual problems. The dual <strong>Simplex Method<\/strong> is a powerful tool for solving problems where the primal is infeasible but the dual is feasible. This advanced concept is often tested in competitive exams.<\/p>\n<h3>4. Apply the Two-Phase Method<\/h3>\n<p>For problems with artificial variables, use the two-phase <strong>Simplex Method<\/strong>. Phase I eliminates artificial variables to find a feasible solution, while Phase II optimizes the objective function. This technique is essential for handling complex LPPs.<\/p>\n<h2>Conclusion: Master the Simplex Method for Exam Success<\/h2>\n<p>The <strong>Simplex Method<\/strong> is a fundamental algorithm for solving linear programming problems, making it a critical topic for UPPSC Assistant Professor aspirants. By understanding its theoretical foundations, practicing step-by-step examples, and applying it to real-world scenarios, candidates can develop a robust command of this optimization technique.<\/p>\n<p>Consistent practice and a structured study strategy are key to mastering the <strong>Simplex Method<\/strong>. Utilize resources like <a href=\"https:\/\/www.vedprep.com\/\">VedPrep<\/a> to access expert guidance, solved examples, and interactive learning tools. With dedication and the right approach, aspirants can confidently tackle <strong>Simplex Method<\/strong> questions in competitive exams and beyond.<\/p>\n<section class=\"vedprep-faq\">\n<h2>Frequently Asked Questions About the Simplex Method<\/h2>\n<h3>Core Understanding<\/h3>\n<div class=\"faq-item\">\n<h4>What is the Simplex Method?<\/h4>\n<p>The <strong>Simplex Method<\/strong> is an iterative algorithm used in operations research to solve linear programming problems. It evaluates the objective function at the vertices of the feasible region to find the optimal solution.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How does the Simplex Method work?<\/h4>\n<p>The <strong>Simplex Method<\/strong> begins by converting the LPP into standard form and constructing a simplex tableau. It iteratively improves the solution by selecting entering and leaving variables until optimality is achieved.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>Why is the Simplex Method important in operations research?<\/h4>\n<p>The <strong>Simplex Method<\/strong> is a cornerstone of operations research, providing a systematic approach to solving complex LPPs. Its efficiency and accuracy make it indispensable for resource optimization and decision-making.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What are the limitations of the Simplex Method?<\/h4>\n<p>The <strong>Simplex Method<\/strong> can struggle with degeneracy and is sensitive to the initial basis. However, advanced techniques like Bland\u2019s rule can mitigate these limitations.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How is the Simplex Method related to LPP?<\/h4>\n<p>The <strong>Simplex Method<\/strong> is specifically designed to solve LPPs by exploiting their linear structure. It efficiently navigates the feasible region to find the optimal solution.<\/p>\n<\/div>\n<h3>Exam Application<\/h3>\n<div class=\"faq-item\">\n<h4>How can the Simplex Method be applied to the UPPSC Assistant Professor exam?<\/h4>\n<p>The <strong>Simplex Method<\/strong> is a key topic in the UPPSC Assistant Professor syllabus. Candidates can apply it to solve LPP-based questions, demonstrating their understanding of optimization techniques.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>What types of questions involve the Simplex Method in competitive exams?<\/h4>\n<p>Exams like CSIR NET and GATE feature questions on the <strong>Simplex Method<\/strong>, including tableau construction, pivot selection, and result interpretation. Mastery of these concepts is essential for success.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How can candidates practice the Simplex Method for exams?<\/h4>\n<p>Candidates should solve past year papers, work through case studies, and use online resources like <a href=\"https:\/\/www.vedprep.com\/\">VedPrep<\/a> to reinforce their understanding of the <strong>Simplex Method<\/strong>.<\/p>\n<\/div>\n<h3>Common Mistakes<\/h3>\n<div class=\"faq-item\">\n<h4>What are common mistakes to avoid when using the Simplex Method?<\/h4>\n<p>Common errors include incorrect tableau construction, misinterpreting results, and failing to check for optimality. Candidates should verify each step to ensure accuracy.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How does degeneracy affect the Simplex Method?<\/h4>\n<p>Degeneracy can cause cycling or stalling in the <strong>Simplex Method<\/strong>. Techniques like Bland\u2019s rule help address this issue and ensure convergence to the optimal solution.<\/p>\n<\/div>\n<h3>Advanced Concepts<\/h3>\n<div class=\"faq-item\">\n<h4>What are advanced topics related to the Simplex Method?<\/h4>\n<p>Advanced topics include the two-phase method, dual <strong>Simplex Method<\/strong>, and the use of artificial variables. These concepts deepen understanding and prepare candidates for complex exam questions.<\/p>\n<\/div>\n<div class=\"faq-item\">\n<h4>How is the Simplex Method used in real-world applications?<\/h4>\n<p>The <strong>Simplex Method<\/strong> is applied in fields like finance, logistics, and energy to optimize resources and make data-driven decisions. Case studies provide practical insights into its applications.<\/p>\n<\/div>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>The Simplex Method is a powerful optimization technique used to solve linear programming problems by iteratively improving the current solution until an optimal solution is reached. It&#8217;s a crucial concept for UPPSC Assistant Professor aspirants, especially for CSIR NET and GATE exams.<\/p>\n","protected":false},"author":12,"featured_media":24080,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":"","_debug_hook_fired":"2026-08-06 07:33:43","rank_math_seo_score":0},"categories":[352],"tags":[2923,20301,2915,2928,20300,20302,20303,20304,2922],"class_list":["post-24081","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uppsc","tag-competitive-exams","tag-linear-programming-problem-lpp","tag-operations-research","tag-simplex-method","tag-simplex-method-for-uppsc-assistant-professor","tag-simplex-method-for-uppsc-assistant-professor-notes","tag-simplex-method-for-uppsc-assistant-professor-questions","tag-simplex-method-for-uppsc-assistant-professor-tips","tag-vedprep","entry","has-media"],"acf":[],"rank_math_title":"Simplex Method 2025: Ultimate Guide for UPPSC Assistant","rank_math_description":"Simplex Method is the proven algorithm for linear programming. Learn step-by-step Simplex Method for UPPSC Assistant Professor, CSIR NET, and GATE exams with.","rank_math_focus_keyword":"Simplex Method","_links":{"self":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts\/24081","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/comments?post=24081"}],"version-history":[{"count":1,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts\/24081\/revisions"}],"predecessor-version":[{"id":33959,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts\/24081\/revisions\/33959"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/media\/24080"}],"wp:attachment":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/media?parent=24081"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/categories?post=24081"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/tags?post=24081"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}