// Numbas version: exam_results_page_options
{"name": "Identify profit and loss from a simultaneous equation graph", "extensions": [], "custom_part_types": [], "resources": [["question-resources/simultaneous_VNJzg0U.png", "/srv/numbas/media/question-resources/simultaneous_VNJzg0U.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Identify profit and loss from a simultaneous equation graph", "tags": [], "metadata": {"description": "<p>Students are asked to find either the initial production cost, or a gradient, or the break even point from a graph.<br />They are then asked to determine the profit or loss from the graph for the production of a particular number of units. This number is randomised.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>The graph shows the cost of producing pencils and the revenue raised by selling them.</p>\n<p><img src=\"resources/question-resources/simultaneous_VNJzg0U.png\"/></p>", "advice": "<p>{advice}</p>\n<p>When {n} units are sold, from the graph, the revenue (income) is equal to {currency(1*n,'\\\\$','')}, and the costs are equal to {currency(0.5*n+20,'\\\\$','')}.</p>\n<p>profit&nbsp;= income - costs = {currency(1*n,'\\\\$','')} -&nbsp;{currency(0.5*n+20,'\\\\$','')} = {currency(profit,'\\\\$','')}.</p>\n<p>A positive number indicates a profit while a negative number indicates a loss.</p>\n<p>The gradient of the cost line is the cost to make one unit.</p>\n<p>The gradient of the income line&nbsp;is the income received from one unit. This is because gradient = rise over run, which is the incomefrom making $n$ units, divided by $n$, which equals the&nbsp;income&nbsp;from one unit.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"questionlist": {"name": "questionlist", "group": "Ungrouped variables", "definition": "[\n  'How many pencils need to be sold to break even?',\n  'What is the production setup cost, in dollars?',\n  'What is the gradient of the revenue line?',\n  'What is the gradient of the cost line?'\n  ]", "description": "", "templateType": "anything", "can_override": false}, "answerlist": {"name": "answerlist", "group": "Ungrouped variables", "definition": "[40,20,1,0.5]", "description": "", "templateType": "anything", "can_override": false}, "idx": {"name": "idx", "group": "Ungrouped variables", "definition": "random(0..3)", "description": "<p>choose between the 4 possible questions.</p>", "templateType": "anything", "can_override": false}, "question": {"name": "question", "group": "Ungrouped variables", "definition": "questionlist[idx]", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "answerlist[idx]", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(1..11)*5", "description": "", "templateType": "anything", "can_override": false}, "profit": {"name": "profit", "group": "Ungrouped variables", "definition": "1*n - (0.5*n+20)", "description": "", "templateType": "anything", "can_override": false}, "advicelist": {"name": "advicelist", "group": "Ungrouped variables", "definition": "[\n'The break even point occurs where the two lines meet. At this point, the number can be read from the horizontal axis, and is equal to 3 boxes.',\n  'The production setup cost is the cost when no boxes are manufactured. This is $20.',\n  'Gradient is rise / run. When the revenue line goes up by 10 units, it goes across by 10 unit, so the gradient is 10 divided by 10 = 1',\n  'Gradient is rise / run. When the revenue line goes up by 5 units, it goes across by 10 unit, so the gradient is 5 divided by 10 = 0.5'\n]", "description": "", "templateType": "anything", "can_override": false}, "advice": {"name": "advice", "group": "Ungrouped variables", "definition": "advicelist[idx]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["questionlist", "answerlist", "idx", "question", "answer", "n", "profit", "advicelist", "advice"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "prompt": "<p>{question}</p>", "minValue": "answer", "maxValue": "answer", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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, "prompt": "<p>What is the profit or loss in dollars when {n}&nbsp;pencils are sold?</p>\n<p>Enter a profit as a positive number (for example, 20) but enter loss as a negative number (for example, -20)</p>", "minValue": "profit", "maxValue": "profit", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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>Write down an equation for the cost graph.&nbsp;</p>\n<p>$c$ represents cost, and $n$ represents the number of pencils made.</p>\n<p>$c = $ [[0]] $\\times n + $ [[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], 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"mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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>Write down an equation for the income line.&nbsp;</p>\n<p>$r$ represents revenue (income), and $n$ represents the number of pencils made.</p>\n<p>$r = $ [[0]] $\\times n$</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, 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represent?</p>\n<p>Write down your answers. You can check your answers after you have completed this question by choosing \"reveal solutions\".</p>"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}