// Numbas version: finer_feedback_settings
{"name": "Musa's copy SIT316 Week 7 - Branch and Bound for integer programming V2-Q2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Musa's copy SIT316 Week 7 - Branch and Bound for integer programming V2-Q2", "tags": [], "metadata": {"description": "<p>This question tests the student's ability to model and solve&nbsp;Integer Programming problems by Branch and bound method</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"kx": {"name": "kx", "group": "part a", "definition": "2*random(6,6.5,7,7.5,8,8.5,9,11,11.5,12,12.5,13,13.5,14)", "description": "", "templateType": "anything", "can_override": false}, "ky": {"name": "ky", "group": "part a", "definition": "20", "description": "", "templateType": "anything", "can_override": false}, "k1": {"name": "k1", "group": "part a", "definition": "random(0.75,0.8,0.85,0.9,0.95)", "description": "", "templateType": "anything", "can_override": false}, "k22": {"name": "k22", "group": "part a", "definition": "random(0.75,0.8,0.85,0.9,0.95)", "description": "", "templateType": "anything", "can_override": false}, "k2": {"name": "k2", "group": "part a", "definition": "random(2,2.2,2.4,2.6,2.8,3)", "description": "", "templateType": "anything", "can_override": false}, "k11": {"name": "k11", "group": "part a", "definition": "random(2,2.2,2.4,2.6,2.8,3)", "description": "", "templateType": "anything", "can_override": false}, "s": {"name": "s", "group": "part a", "definition": "k2*a+k1*b+k1*k2", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "part a", "definition": "random(5..15)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "part a", "definition": "random(5..15)", "description": "", "templateType": "anything", "can_override": false}, "ss": {"name": "ss", "group": "part a", "definition": "k22*a+k11*b+k11*k22", "description": "", "templateType": "anything", "can_override": false}, "fsol": {"name": "fsol", "group": "part a", "definition": "kx*xsol + ky*ysol", "description": "", "templateType": "anything", "can_override": true}, "xsol": {"name": "xsol", "group": "part a", "definition": "if(kx<20,a-1,a+1)", "description": "", "templateType": "anything", "can_override": false}, "ysol": {"name": "ysol", "group": "part a", "definition": "if(kx<20,b+1,b-1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "part a", "variables": ["kx", "ky", "k1", "k22", "k2", "k11", "s", "a", "b", "ss", "fsol", "xsol", "ysol"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><strong>Solve the following Integer Programming problem by Branch and Bound Maximization method.</strong></p>\n<p></p>\n<p><strong>Minimize</strong>: $\\simplify{-{kx} x - {ky} y}$</p>\n<p><strong>Subject to</strong></p>\n<p>$ \\simplify{20*{k2} x&nbsp; + 20*{k1} y} \\le&nbsp; \\var{20*s}$</p>\n<p>$ \\simplify{-20*{k22} x - 20*{k11}y} \\ge -\\var{20*ss} $</p>\n<p>$x,y \\ge 0$ and integers</p>\n<p></p>\n<p><strong>Submitting your results:</strong></p>\n<ol>\n<li>Click on \"<strong>End Exam\"</strong> and \"<strong>Print this results summary\" </strong>(your problem will be extracted as a pdf file with all the necessary information/data). <strong>Do not worry</strong> about the \"<strong>Total 0/0 (0%)</strong>\" score, this pdf is only for generating a LP problem {k1}{fsol}{xsol}{ysol}).</li>\n<li>Solve the problem by \"Branch and Bound Maximization\" method by hand, for example, as in the examples included in \"Knowledge Reinforcement\".\n<div class=\"d2l-editable d2l-editable-autosize\" id=\"d2l_9_4_733\" title=\"Edit module title\"></div>\n</li>\n<li>This methods requires solving some <strong>Continuous</strong> optimisation problem at each step. You can use any <strong>Computational Packages </strong>for finding optimal solution to these continous optimisation problems and <strong>do not need to include your code </strong>(just use the output-solution); or alternatively, you can solve them by geometric method by hand.</li>\n</ol>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{kx*a + ky*b}", "maxValue": "{kx*a + ky*b}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}]}