// Numbas version: exam_results_page_options
{"name": "Transportation problem - apply minimum cost algorithm to unbalanced problem", "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", "omit_source", "show_sources", "show_destinations"], "name": "Setup"}, {"variables": ["supply", "demand", "costs", "show_supply", "show_demand", "show_costs", "dummy_resource"], "name": "Initial data"}, {"variables": ["assignment", "assignment_cost", "show_assignment"], "name": "Minimum costs"}], "variables": {"show_assignment": {"group": "Minimum costs", "templateType": "anything", "definition": "matrix(map(\n  map(\n    assignment[x][y],\n    y,\n    0..show_destinations-1\n  ),\n  x,\n  0..show_sources-1\n))", "description": "", "name": "show_assignment"}, "costs": {"group": "Initial data", "templateType": "anything", "definition": "matrix(map(\n  map(\n    if(x<show_sources and y<show_destinations,\n        random(1..9),\n        0\n    ),\n    y,\n    0..num_destinations-1\n  ),\n  x,\n  0..num_sources-1\n))", "description": "", "name": "costs"}, "show_sources": {"group": "Setup", "templateType": "anything", "definition": "num_sources-if(omit_source,1,0)", "description": "", "name": "show_sources"}, "omit_source": {"group": "Setup", "templateType": "anything", "definition": "random(true,false)", "description": "", "name": "omit_source"}, "num_destinations": {"group": "Setup", "templateType": "anything", "definition": "4", "description": "", "name": "num_destinations"}, "show_supply": {"group": "Initial data", "templateType": "anything", "definition": "supply[0..show_sources]", "description": "", "name": "show_supply"}, "supply": {"group": "Initial data", "templateType": "anything", "definition": "random_partition(total,num_sources)", "description": "", "name": "supply"}, "show_destinations": {"group": "Setup", "templateType": "anything", "definition": "num_destinations-if(omit_source,0,1)", "description": "", "name": "show_destinations"}, "dummy_resource": {"group": "Initial data", "templateType": "anything", "definition": "if(omit_source,\n  sum(supply)-sum(show_supply),\n  sum(demand)-sum(show_demand)\n)", "description": "", "name": "dummy_resource"}, "num_sources": {"group": "Setup", "templateType": "anything", "definition": "random(3..5)", "description": "", "name": "num_sources"}, "show_demand": {"group": "Initial data", "templateType": "anything", "definition": "demand[0..show_destinations]", "description": "", "name": "show_demand"}, "show_costs": {"group": "Initial data", "templateType": "anything", "definition": "matrix(map(map(costs[x][y],y,0..show_destinations-1),x,0..show_sources-1))", "description": "", "name": "show_costs"}, "assignment_cost": {"group": "Minimum costs", "templateType": "anything", "definition": "assignment_cost(assignment,costs)", "description": "", "name": "assignment_cost"}, "total": {"group": "Setup", "templateType": "anything", "definition": "random(50..500)", "description": "", "name": "total"}, "assignment": {"group": "Minimum costs", "templateType": "anything", "definition": "minimum_cost(supply,demand,costs)", "description": "", "name": "assignment"}, "demand": {"group": "Initial data", "templateType": "anything", "definition": "random_partition(total,num_destinations)", "description": "", "name": "demand"}}, "ungrouped_variables": [], "name": "Transportation problem - apply minimum cost algorithm to unbalanced problem", "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"]]}}, "parts": [{"showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "<p>By adding dummy sources or destinations, balance this problem.</p>\n<p>The balanced problem adds&nbsp;another&nbsp;[[0]] with&nbsp;[[1]] units of coal.</p>\n<p>Enter the cost matrix for the balanced problem below.</p>\n<p>[[2]]</p>", "unitTests": [], "showFeedbackIcon": true, "scripts": {}, "gaps": [{"displayType": "radiogroup", "showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "matrix": "if(omit_source,[1,0],[0,1])", "choices": ["<p>pit</p>", "<p>power station</p>"], "unitTests": [], "variableReplacements": [], "shuffleChoices": false, "showFeedbackIcon": true, "scripts": {}, "minMarks": 0, "type": "1_n_2", "maxMarks": 0, "variableReplacementStrategy": "originalfirst", "displayColumns": 0, "marks": 0}, {"showCorrectAnswer": true, "allowFractions": false, "customMarkingAlgorithm": "", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "minValue": "dummy_resource", "maxValue": "dummy_resource", "unitTests": [], "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "scripts": {}, "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "variableReplacements": [], "marks": 1, "mustBeReducedPC": 0}, {"showCorrectAnswer": true, "markPerCell": false, "allowFractions": false, "correctAnswer": "costs", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowResize": true, "unitTests": [], "correctAnswerFractions": false, "numRows": 1, "scripts": {}, "type": "matrix", "numColumns": 1, "tolerance": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 1, "showFeedbackIcon": true}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "sortAnswers": false}, {"scripts": {}, "showCorrectAnswer": true, "markPerCell": false, "allowFractions": false, "correctAnswer": "show_assignment", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "prompt": "<p>Apply the minimum cost algorithm to your balanced problem 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>", "unitTests": [], "correctAnswerFractions": false, "numRows": "show_sources", "allowResize": false, "type": "matrix", "numColumns": "show_destinations", "tolerance": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [{"part": "p0g2", "must_go_first": false, "variable": "costs"}], "marks": 1, "showFeedbackIcon": true}, {"showCorrectAnswer": true, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "<p>What is the total cost of this solution?</p>\n<p>&pound;&nbsp;[[0]]</p>", "unitTests": [], "showFeedbackIcon": true, "scripts": {}, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "customMarkingAlgorithm": "", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "minValue": "assignment_cost", "maxValue": "assignment_cost", "unitTests": [], "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "scripts": {}, "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "variableReplacements": [{"part": "p1", "must_go_first": false, "variable": "assignment"}], "marks": 1, "mustBeReducedPC": 0}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "sortAnswers": false}], "statement": "<p>Four power stations labelled $j = 1,2,3,4$ require {show_variable_list(show_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(show_supply,'a')} units of coal, respectively.</p>\n<p>The cost $c_{ij}$, in pounds, 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(show_supply,show_demand,show_costs)}</p>", "tags": [], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Although the statement has 4 power stations and 3 pits, when the question is run sometimes 3 power stations are given and sometimes 4 pits.</p>"}, "extensions": ["optimisation"], "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<h4>a)</h4>\n<p>The total supply is {sum(show_supply)}, while the total demand is {sum(show_demand)}, so we need to add a dummy {if(omit_source,'pit supplying','power station demanding')} {dummy_resource} units of coal.</p>\n<p>The cost matrix&nbsp;then looks like this:</p>\n<p>{cost_table(supply,demand,costs)}</p>\n<h4>b)</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>c)</h4>\n<p>The total cost of this solution&nbsp;is $\\var{show_cost_calculation(assignment,costs)}$.</p>", "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}