// Numbas version: exam_results_page_options
{"name": "Transportation problem - apply minimum cost algorithm", "extensions": ["optimisation"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [{"variables": ["num_sources", "num_destinations", "total"], "name": "Setup"}, {"variables": ["supply", "demand", "costs"], "name": "Initial data"}, {"variables": ["assignment", "assignment_cost"], "name": "Minimum costs"}], "variables": {"costs": {"templateType": "anything", "group": "Initial data", "definition": "matrix(repeat(\n  repeat(\n    random(1..9),\n    num_destinations\n  ),\n  num_sources\n))", "description": "", "name": "costs"}, "num_sources": {"templateType": "anything", "group": "Setup", "definition": "random(3..5)", "description": "", "name": "num_sources"}, "num_destinations": {"templateType": "anything", "group": "Setup", "definition": "7-num_sources+random(0,1)", "description": "", "name": "num_destinations"}, "assignment": {"templateType": "anything", "group": "Minimum costs", "definition": "minimum_cost(supply,demand,costs)", "description": "", "name": "assignment"}, "assignment_cost": {"templateType": "anything", "group": "Minimum costs", "definition": "assignment_cost(assignment,costs)", "description": "", "name": "assignment_cost"}, "total": {"templateType": "anything", "group": "Setup", "definition": "random(50..500)", "description": "", "name": "total"}, "supply": {"templateType": "anything", "group": "Initial data", "definition": "random_partition(total,num_sources)", "description": "", "name": "supply"}, "demand": {"templateType": "anything", "group": "Initial data", "definition": "random_partition(total,num_destinations)", "description": "", "name": "demand"}}, "ungrouped_variables": [], "rulesets": {}, "name": "Transportation problem - apply minimum cost algorithm", "functions": {"show_variable_list": {"type": "string", "language": "javascript", "definition": "return data.map(function(n,i) {\n  return '$'+name+'_{'+(i+1)+'} = '+Numbas.math.niceNumber(n)+'$';\n}).join(', ');", "parameters": [["data", "list"], ["name", "string"]]}}, "showQuestionGroupNames": false, "parts": [{"showCorrectAnswer": true, "markPerCell": false, "allowFractions": false, "correctAnswer": "assignment", "allowResize": false, "prompt": "<p>Apply the minimum cost algorithm to find an assignment of units of coal to be&nbsp;transported between pits and power stations.</p>\n<p>When there's more than one choice of cell, choose the cell with the maximum available allocation.</p>", "correctAnswerFractions": false, "numRows": "num_sources", "scripts": {}, "type": "matrix", "numColumns": "num_destinations", "tolerance": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1}, {"showCorrectAnswer": true, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "minValue": "assignment_cost", "prompt": "<p>What is the total cost of this solution?</p>", "showPrecisionHint": false, "scripts": {}, "type": "numberentry", "correctAnswerFraction": false, "variableReplacements": [{"part": "p0", "must_go_first": false, "variable": "assignment"}], "marks": 1, "maxValue": "assignment_cost"}], "variablesTest": {"condition": "", "maxRuns": "3000"}, "statement": "<p>Four power stations labelled $j = 1,2,3,4$ require {show_variable_list(demand,'b')} units of coal, respectively. These are to be provided by three pits labelled $i=1,2,3$, which have supplies of {show_variable_list(supply,'a')} units of coal, respectively.</p>\n<p>The cost $c_{ij}$ of transporting one unit of coal from pit $i$ to power station $j$ is in the following table (with supplies and demand shown in the margin).</p>\n<p>{cost_table(supply,demand,costs)}</p>", "tags": [], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": ""}, "advice": "<h4>a)</h4>\n<p>The following tables show each step of the minimum cost algorithm:</p>\n<p>{minimum_cost_display(supply,demand,costs)}</p>\n<h4>b)</h4>\n<p>The total cost of this solution&nbsp;is $\\var{show_cost_calculation(assignment,costs)}$.</p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}