// Numbas version: exam_results_page_options
{"name": "Luis's copy of Solve a linear programming problem", "extensions": ["jsxgraph", "optimisation"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": ["jsxgraph", "optimisation"], "statement": "<p>{business_long}<span data-jme-visible=\"business_short&lt;&gt;&quot;&quot;\"> ({business_short})</span> makes two products: {product_1s} and {product_2s}.</p>\n<p>Existing orders require {business} to make at least <strong>{xconstraint}</strong> {product_1s} and <strong>{yconstraint}</strong> {product_2s} each day.</p>\n<p>Each unit of {product_1s} produced uses&nbsp;<strong>{resource1x}</strong> {resource_1_units} {resource_1}&nbsp;and&nbsp;<strong>{resource2x}</strong> {resource_2_units} {resource_2}.</p>\n<p>Each unit of {product_2s} produced uses&nbsp;<strong>{resource1y}</strong> {resource_1_units}&nbsp;{resource_1}&nbsp;and&nbsp;<strong>{resource2y}</strong> {resource_2_units} {resource_2}.</p>\n<p>However, the resources are limited: {business} can only obtain <strong>{totalresource1}</strong> {resource_1_units} {resource_1} and <strong>{totalresource2}</strong>&nbsp;{resource_2_units} {resource_2}&nbsp;each day.</p>\n<p>Each sale of a unit of {product_1s} gives <strong>&pound;{profitx}</strong> profit. Each sale of a unit of {product_2s} gives <strong>&pound;{profity}</strong> profit.</p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": ["constraints", "linear programming", "objective function", "template"], "metadata": {"description": "<p>Student is given a set of constraints for a linear program. Asked to enter the constraints as inequalities, and then to identify the optimal solution.</p>\n<p>Problem with solving the simultaneous equations gven by the constraints - too unwieldy and not given enough marks for doing so. Best if the point of intersection is given graphically by putting the mouse over the intersection.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"showFeedbackIcon": true, "customMarkingAlgorithm": "", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "gaps": [{"showFeedbackIcon": true, "allowFractions": false, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "variableReplacements": [], "minValue": "xconstraint", "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 1, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "maxValue": "xconstraint", "correctAnswerStyle": "plain"}, {"showFeedbackIcon": true, "allowFractions": false, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "variableReplacements": [], "minValue": "yconstraint", "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 1, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "maxValue": "yconstraint", "correctAnswerStyle": "plain"}], "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "scripts": {}, "prompt": "<p>Let $x$, $y$ be the number of units of {product_1s} and {product_2s} produced, respectively.</p>\n<p>What are the constraints on production resulting from the existing orders?</p>\n<p>$x \\geq$&nbsp;[[0]]</p>\n<p>$y \\geq$&nbsp;[[1]]</p>"}, {"showFeedbackIcon": true, "customMarkingAlgorithm": "", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "gaps": [{"showFeedbackIcon": true, "allowFractions": false, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "variableReplacements": [], "minValue": "resource1x", "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 1, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "maxValue": "resource1x", "correctAnswerStyle": "plain"}, {"showFeedbackIcon": true, "allowFractions": false, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "variableReplacements": [], "minValue": "resource1y", "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 1, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "maxValue": "resource1y", "correctAnswerStyle": "plain"}, {"showFeedbackIcon": true, "allowFractions": false, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "variableReplacements": [], "minValue": "totalresource1", "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 1, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "maxValue": "totalresource1", "correctAnswerStyle": "plain"}, {"showFeedbackIcon": true, "allowFractions": false, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "variableReplacements": [], "minValue": "resource2x", "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 1, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "maxValue": "resource2x", "correctAnswerStyle": "plain"}, {"showFeedbackIcon": true, "allowFractions": false, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "variableReplacements": [], "minValue": "resource2y", "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 1, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "maxValue": "resource2y", "correctAnswerStyle": "plain"}, {"showFeedbackIcon": true, "allowFractions": false, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "variableReplacements": [], "minValue": "totalresource2", "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 1, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "maxValue": "totalresource2", "correctAnswerStyle": "plain"}], "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "scripts": {}, "prompt": "<p>Now enter&nbsp;the constraints given by the availability of {resource_1}&nbsp;and {resource_2}:</p>\n<p>{capitalise(resource_1)}: [[0]]&nbsp;$x + $&nbsp;[[1]]&nbsp;$y \\le $&nbsp;[[2]]</p>\n<p>{capitalise(resource_2)}: [[3]]&nbsp;$x + $&nbsp;[[4]]&nbsp;$y \\le $&nbsp;[[5]]</p>"}, {"showFeedbackIcon": true, "customMarkingAlgorithm": "", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "gaps": [{"checkVariableNames": false, "showFeedbackIcon": true, "marks": 1, "customMarkingAlgorithm": "", "showPreview": true, "answerSimplification": "all", "expectedVariableNames": [], "checkingAccuracy": 0.001, "failureRate": 1, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "checkingType": "absdiff", "extendBaseMarkingAlgorithm": true, "unitTests": [], "vsetRange": [0, 1], "type": "jme", "showCorrectAnswer": true, "vsetRangePoints": 5, "scripts": {}, "answer": "{profitx}*x+{profity}*y"}], "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "scripts": {}, "prompt": "<p>Given the information on profits for {product_1s} and {product_2s}, write down&nbsp;the objective function which is to be maximised:&nbsp;[[0]]</p>"}, {"showFeedbackIcon": true, "customMarkingAlgorithm": "", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "gaps": [{"showFeedbackIcon": true, "allowFractions": false, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacementStrategy": "alwaysreplace", "correctAnswerFraction": false, "variableReplacements": [{"part": "p0g0", "variable": "xconstraint", "must_go_first": true}, {"part": "p0g1", "variable": "yconstraint", "must_go_first": true}, {"part": "p1g0", "variable": "resource1x", "must_go_first": true}, {"part": "p1g1", "variable": "resource1y", "must_go_first": true}, {"part": "p1g2", "variable": "totalresource1", "must_go_first": true}, {"part": "p1g3", "variable": "resource2x", "must_go_first": true}, {"part": "p1g4", "variable": "resource2y", "must_go_first": true}, {"part": "p1g5", "variable": "totalresource2", "must_go_first": true}], "minValue": "best_x", "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 1, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "maxValue": "best_x", "correctAnswerStyle": "plain"}, {"showFeedbackIcon": true, "allowFractions": false, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacementStrategy": "alwaysreplace", "correctAnswerFraction": false, "variableReplacements": [{"part": "p0g0", "variable": "xconstraint", "must_go_first": true}, {"part": "p0g1", "variable": "yconstraint", "must_go_first": true}, {"part": "p1g0", "variable": "resource1x", "must_go_first": true}, {"part": "p1g1", "variable": "resource1y", "must_go_first": true}, {"part": "p1g2", "variable": "totalresource1", "must_go_first": true}, {"part": "p1g3", "variable": "resource2x", "must_go_first": true}, {"part": "p1g4", "variable": "resource2y", "must_go_first": true}, {"part": "p1g5", "variable": "totalresource2", "must_go_first": true}], "minValue": "best_y", "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 1, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "maxValue": "best_y", "correctAnswerStyle": "plain"}, {"showFeedbackIcon": true, "allowFractions": false, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "variableReplacements": [{"part": "p3g0", "variable": "best_x", "must_go_first": false}, {"part": "p3g1", "variable": "best_y", "must_go_first": false}], "minValue": "best_profit", "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 1, "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "maxValue": "best_profit", "correctAnswerStyle": "plain"}], "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "scripts": {}, "prompt": "<p><span class=\"lp-graph\">Input diagram goes here</span></p>\n<p>Drag the objective line on the diagram above to find the position which gives the maximum profit.</p>\n<p>Round your answers down to the nearest integer, end enter them below:</p>\n<p>Produce&nbsp;[[0]] {product_1s} and&nbsp;[[1]] {product_2s}, earning &pound;&nbsp;[[2]]&nbsp;in profit.</p>"}], "ungrouped_variables": [], "name": "Luis's copy of Solve a linear programming problem", "advice": "<h4>a)</h4>\n<p>The existing orders give two constraints:</p>\n<p>\\begin{align} <br/>x &amp;\\geq \\var{xconstraint} \\\\<br/> y &amp;\\geq \\var{yconstraint}<br/>\\end{align}</p>\n<h4>b)</h4>\n<p>The limits on the two resources, and the amounts of each resource used to produce a unit of each product, give two further constraints:</p>\n<p>\\begin{align} <br/>\\simplify{{resource1x}x + {resource1y}y} &amp;\\leq \\var{totalresource1} \\\\<br/>\\simplify{{resource2x}x + {resource2y}y} &amp;\\leq \\var{totalresource2}<br/>\\end{align}</p>\n<h4>c)</h4>\n<p>The objective function to be maximised is the total profit earned, that is, the sum of the profits earned from each unit made:</p>\n<p>\\[&nbsp;\\simplify{{profitx}x + {profity}y} \\]</p>\n<h4>d)</h4>\n<p><span id=\"advicediagram\">The solution graph goes here</span></p>\n<p>It is clear that the minimum profit is given by producing enough {product_1s} and {product_2s} so that the existing demand is met and no more. You can see this by moving the objective function line down to the intersection of the two minimum constraint lines - there are no other points inside the feasible region under the objective line.</p>\n<p>Next, drag the objective function line upwards until&nbsp;there are no points above the objective line in the feasible region. At this point, the objective line touches the intersection of the lines representing the constraints&nbsp;for {line_names[best_lines[0]]} and {line_names[best_lines[1]]}.</p>\n<p>You can find the coordinates of this point by solving the equations for these two lines:</p>\n<p><span data-jme-visible=\"best_lines[0]=0\">\\[ \\simplify{{resource1x}x + {resource1y}y = {totalresource1}} \\]</span><span data-jme-visible=\"best_lines[0]=1\">\\[ \\simplify{{resource2x}x + {resource2y}y = {totalresource2}} \\]</span></p>\n<p><span data-jme-visible=\"best_lines[1]=1\">\\[ \\simplify{{resource2x}x + {resource2y}y = {totalresource2}} \\]</span><span data-jme-visible=\"best_lines[1]=2\">\\[ x = \\var{xconstraint} \\]</span><span data-jme-visible=\"best_lines[1]=3\">\\[ y = \\var{yconstraint} \\]</span></p>\n<p>The solution to this system of equations is $x = \\var{best_x}$, $y = \\var{best_y}$, giving a profit of</p>\n<p>\\[ \\text{Profit} =&nbsp;\\simplify[]{{profitx}*{best_x} + {profity}*{best_y}} = \\text{&pound;}\\var{best_profit} \\]</p>", "variables": {"best_profit_float": {"name": "best_profit_float", "definition": "profit(best_x_float,best_y_float)", "group": "Optimum strategy", "description": "<p>The profit at the best intersection point, if fractions of units are allowed</p>", "templateType": "anything"}, "constraint2xvalue": {"name": "constraint2xvalue", "definition": "round(scalingfactor2*resource2y+xconstraint)", "group": "Bounds", "description": "<p>Where the constraint line for resource 2 cuts the y-constraint</p>", "templateType": "anything"}, "resource2y": {"name": "resource2y", "definition": "\nrandom(1500..3000#100)", "group": "Constraints", "description": "<p>How much of resource 2 the second product uses per unit</p>", "templateType": "anything"}, "totalresource2": {"name": "totalresource2", "definition": "siground(\n  scalingfactor2*resource2x*resource2y +\n  resource2y*yconstraint +\n  resource2x*xconstraint\n,3)", "group": "Constraints", "description": "<p>Total amount of resource 2 available</p>", "templateType": "anything"}, "constraint1yvalue": {"name": "constraint1yvalue", "definition": "r2+constraint2yvalue", "group": "Bounds", "description": "<p>Where line given by resource 1 constraint cuts the x-constraint line.</p>\n<p>It is always greater than the point at which the second resource line cuts.</p>", "templateType": "anything"}, "resource_1_units": {"name": "resource_1_units", "definition": "\"kg\"", "group": "Text strings", "description": "<p>Dimension of the first resource</p>", "templateType": "string"}, "product_1s": {"name": "product_1s", "definition": "\"bulletproof tea cosies\"", "group": "Text strings", "description": "<p>Plural name of the first product</p>", "templateType": "string"}, "best_y": {"name": "best_y", "definition": "floor(best_y_float)", "group": "Optimum strategy", "description": "<p>The integer number of units of the second&nbsp;product to produce to earn the highest profit</p>", "templateType": "anything"}, "resource1y": {"name": "resource1y", "definition": "random(50..70)", "group": "Constraints", "description": "<p>How much of resource 1 the second product uses per unit</p>", "templateType": "anything"}, "xconstraint": {"name": "xconstraint", "definition": "\nrandom(4..10)", "group": "Constraints", "description": "<p>Minimum production of&nbsp;the first product</p>", "templateType": "anything"}, "resource_2_units": {"name": "resource_2_units", "definition": "\"tonnes\"", "group": "Text strings", "description": "<p>Dimension of the second resource</p>", "templateType": "string"}, "best_x_float": {"name": "best_x_float", "definition": "intersection_points[best_point][0]", "group": "Optimum strategy", "description": "<p>The number of units of X to produce&nbsp;to earn the highest profit, if fractions are allowed</p>", "templateType": "anything"}, "constraint2yvalue": {"name": "constraint2yvalue", "definition": "r1+yconstraint", "group": "Bounds", "description": "<p>Where the constraint line for the second resource cuts the x-constraint.</p>\n<p>Second resource line cuts x-constraint at a point greater than the y-constraint</p>", "templateType": "anything"}, "constraint1xvalue": {"name": "constraint1xvalue", "definition": "round(scalingfactor1*resource1y+xconstraint)", "group": "Bounds", "description": "<p>Where the constraint line for resource 1 crosses the y-constraint</p>", "templateType": "anything"}, "profity": {"name": "profity", "definition": "//the coeff of y in the objective function\nceil(profitx*(resource1y/resource1x)*random(1.5..3))", "group": "Profit", "description": "<p>Profit for each unit of the second product sold</p>", "templateType": "anything"}, "r1": {"name": "r1", "definition": "random(10..20)", "group": "Constraints", "description": "<p>The second constraint line cuts the x-constraint line at this value more than the y-constraint</p>", "templateType": "anything"}, "best_profit": {"name": "best_profit", "definition": "profit(best_x,best_y)", "group": "Optimum strategy", "description": "<p>The profit at the best intersection point</p>", "templateType": "anything"}, "product_2": {"name": "product_2", "definition": "\"double-edged cardigan\"", "group": "Text strings", "description": "<p>Singular name of the second product</p>", "templateType": "string"}, "resource2x": {"name": "resource2x", "definition": "\nrandom(250..450#10)", "group": "Constraints", "description": "<p>How much of resource 2 the first product uses per unit</p>", "templateType": "anything"}, "resource_2": {"name": "resource_2", "definition": "\"iron\"", "group": "Text strings", "description": "<p>The name of the second resource</p>", "templateType": "string"}, "line_names": {"name": "line_names", "definition": "[ \"the amount of resource 1 used\", \"the amount of resource 2 used\", \"the minimum amount of X produced\", \"the maximum amount of Y produced\" ]", "group": "Optimum strategy", "description": "<p>Names of the lines, coded as in the definition of <code>best_lines</code></p>", "templateType": "list of strings"}, "business_short": {"name": "business_short", "definition": "\"AMS\"", "group": "Text strings", "description": "<p>A shorter name for the business, to be repeated throughout the text. If the business name is short enough for repeated use, leave this empty.</p>", "templateType": "string"}, "resource_1": {"name": "resource_1", "definition": "\"wool\"", "group": "Text strings", "description": "<p>The name of the first resource</p>", "templateType": "string"}, "best_lines": {"name": "best_lines", "definition": "[[0,2],[1,2],[0,3],[1,3],[0,1]][best_point]", "group": "Optimum strategy", "description": "<p>Which lines are involed in the best point? Coded as follows:</p>\n<p>0 - resource 1</p>\n<p>1 - resource 2</p>\n<p>2 - minimum x</p>\n<p>3 - minimum y</p>\n<p>Note that (minimum x,minimum y) is never the best point</p>", "templateType": "anything"}, "boundx": {"name": "boundx", "definition": "max(constraint1xvalue,constraint2xvalue)", "group": "Bounds", "description": "<p>Right bound of the diagram</p>", "templateType": "anything"}, "yconstraint": {"name": "yconstraint", "definition": "random(4..10)", "group": "Constraints", "description": "<p>Minimum production of the second product</p>", "templateType": "anything"}, "scalingfactor2": {"name": "scalingfactor2", "definition": "precround((r1)/resource2x,2)", "group": "Constraints", "description": "", "templateType": "anything"}, "scalingfactor1": {"name": "scalingfactor1", "definition": "precround((r1+r2)/resource1x,1)", "group": "Constraints", "description": "", "templateType": "anything"}, "r2": {"name": "r2", "definition": "random(5..15)", "group": "Constraints", "description": "<p>The first constraint line cuts the x-constraint line at this value greater than where the second constraint cuts.</p>", "templateType": "anything"}, "business_long": {"name": "business_long", "definition": "\"Amalgamated Mines and Sheep, Inc.\"", "group": "Text strings", "description": "<p>The full name of the business</p>", "templateType": "string"}, "profits": {"name": "profits", "definition": "map(let(x,p[0],y,p[1],profitx*x+profity*y),p,intersection_points)", "group": "Optimum strategy", "description": "<p>Profit earned at each intersection point</p>", "templateType": "anything"}, "best_y_float": {"name": "best_y_float", "definition": "intersection_points[best_point][1]", "group": "Optimum strategy", "description": "<p>The number of units of the second product to produce to earn the highest profit, if fractions are allowed</p>", "templateType": "anything"}, "product_1": {"name": "product_1", "definition": "\"bulletproof tea cosy\"", "group": "Text strings", "description": "<p>Singular name of the first product</p>", "templateType": "string"}, "totalresource1": {"name": "totalresource1", "definition": "siground(\n  scalingfactor1*resource1x*resource1y +\n  resource1y*yconstraint +\n  resource1x*xconstraint\n,3)", "group": "Constraints", "description": "<p>Total amount of resource 1 available</p>", "templateType": "anything"}, "possible_points": {"name": "possible_points", "definition": "filter(\n  let(x,floor(intersection_points[j][0]),y,floor(intersection_points[j][1]),\n    resource1x*x+resource1y*y <= totalresource1+1 and \n    resource2x*x+resource2y*y <= totalresource2+1 and\n    x>=xconstraint and\n    y>=yconstraint\n  ),\n  j,\n  0..len(intersection_points)-1\n)", "group": "Optimum strategy", "description": "<p>Indices of intersection points which satisfy all the constraints.</p>", "templateType": "anything"}, "resource1x": {"name": "resource1x", "definition": "random(20..40)", "group": "Constraints", "description": "<p>How much of resource 1 the first product uses per unit</p>", "templateType": "anything"}, "intersection_points": {"name": "intersection_points", "definition": "[\n  [xconstraint, (totalresource1-resource1x*xconstraint)/resource1y],  //resource 1 intersecting with minimum x\n  [xconstraint, (totalresource2-resource2x*xconstraint)/resource2y],  //resource 2 intersecting with minimum x\n  [(totalresource1-resource1y*yconstraint)/resource1x, yconstraint],  //resource 1 intersecting with minimum y\n  [(totalresource2-resource2y*yconstraint)/resource2x, yconstraint],  //resource 2 intersecting with minimum y\n  let(y, (totalresource1-totalresource2*resource1x/resource2x)/(resource1y - resource1x/resource2x * resource2y),\n    [(totalresource1-resource1y*y)/resource1x, y]  // intersection of the two resource constraints\n  )\n]", "group": "Optimum strategy", "description": "<p>Intersection points of the constraints - the optimum strategy will be one of these</p>", "templateType": "anything"}, "business": {"name": "business", "definition": "if(business_short=\"\",business_long,business_short)", "group": "Text strings", "description": "", "templateType": "anything"}, "best_x": {"name": "best_x", "definition": "floor(best_x_float)", "group": "Optimum strategy", "description": "<p>The integer number of units of the first product to produce to earn the highest profit</p>", "templateType": "anything"}, "boundy": {"name": "boundy", "definition": "max(constraint1yvalue,constraint2yvalue)", "group": "Bounds", "description": "<p>Upper&nbsp;bound of the diagram</p>", "templateType": "anything"}, "profitx": {"name": "profitx", "definition": "//the coeff of x in the objective function\nrandom(2..4)", "group": "Profit", "description": "<p>Profit for each unit of the first product sold</p>", "templateType": "anything"}, "best_point": {"name": "best_point", "definition": "best_by(possible_points,profits)", "group": "Optimum strategy", "description": "<p>The index of the valid intersection point with the highest profit</p>", "templateType": "anything"}, "product_2s": {"name": "product_2s", "definition": "\"double-edged cardigans\"", "group": "Text strings", "description": "<p>Plural name of the second product</p>", "templateType": "string"}}, "preamble": {"js": "function userinput_diagram() {\n\nwith(question.unwrappedVariables) {\n\n  var options = {\n    x_bound: boundx, \n    y_bound: boundy\n  };\n\n  options.objective_line_coordinates = [[0,0],[1,-profitx/profity]];\n  \n  function getStudentAnswer(path) {\n    var part = question.getPart(path);\n    return ko.computed(function() {\n        return parseFloat(part.display.studentAnswer());\n    });\n  }\n  \n  options.minimum_x = getStudentAnswer('p0g0');\n  options.minimum_y = getStudentAnswer('p0g1');\n\n  var x_coefficient_1 = getStudentAnswer('p1g0');\n  var y_coefficient_1 = getStudentAnswer('p1g1');\n  var total_1 = getStudentAnswer('p1g2');\n  options.inequality_1_coordinates = [ko.computed(function() {\n    return [-total_1(),x_coefficient_1(),y_coefficient_1()];\n  })];\n\n  options.inequality_1_ok = ko.computed(function() {\n      return !(isNaN(x_coefficient_1()) || isNaN(y_coefficient_1()) || isNaN(total_1()));\n  });\n\n  var x_coefficient_2 = getStudentAnswer('p1g3');\n  var y_coefficient_2 = getStudentAnswer('p1g4');\n  var total_2 = getStudentAnswer('p1g5');\n  options.inequality_2_coordinates = [ko.computed(function() {\n    return [-total_2(),x_coefficient_2(),y_coefficient_2()];\n  })];\n\n  options.inequality_2_ok = ko.computed(function() {\n      return !(isNaN(x_coefficient_2()) || isNaN(y_coefficient_2()) || isNaN(total_2()));\n  });\n\n  var result = Numbas.extensions.optimisation.linear_programming_board(options);\n  $(question.display.html).find('.lp-graph').html('').append(result.div);\n}\n}\n\nfunction advice_diagram() {\nwith(question.unwrappedVariables) {\n\n  var result = Numbas.extensions.optimisation.linear_programming_board({\n    x_bound: boundx,\n    y_bound: boundy,\n    objective_line_coordinates: [[0,best_profit_float/profity],[1,(best_profit_float-profitx)/profity]],\n    minimum_x: xconstraint,\n    minimum_y: yconstraint,\n    inequality_1_coordinates: [-totalresource1, resource1x, resource1y],\n    inequality_2_coordinates: [-totalresource2, resource2x, resource2y]\n  });\n  $(question.display.html).find('#advicediagram').html('').append(result.div);\n}\n}\n\nquestion.signals.on('HTMLAttached',function() {\n  userinput_diagram();\n  advice_diagram();\n});\n", "css": ""}, "functions": {"profit": {"language": "jme", "definition": "profitx*x+profity*y", "parameters": [["x", "number"], ["y", "number"]], "type": "number"}, "best_by": {"language": "javascript", "definition": "// l1 is a list of indices on l2\n// return the element of l1 which has the biggest corresponding value in l2 \n// (i.e. i such that l2[l1[i]] is biggest)\n\nvar best_1 = null;\nvar best_2 = null;\nfor(var i=0;i<l1.length;i++) {\n  if(best_1===null || l2[l1[i]]>best_2) {\n    best_2 = l2[l1[i]];\n    best_1 = l1[i];\n  }\n}\nreturn best_1", "parameters": [["l1", "list"], ["l2", "list"]], "type": "number"}}, "rulesets": {}, "variable_groups": [{"name": "Constraints", "variables": ["xconstraint", "yconstraint", "resource1x", "resource1y", "resource2x", "resource2y", "r1", "r2", "scalingfactor1", "scalingfactor2", "totalresource1", "totalresource2"]}, {"name": "Bounds", "variables": ["boundx", "boundy", "constraint1xvalue", "constraint1yvalue", "constraint2xvalue", "constraint2yvalue"]}, {"name": "Profit", "variables": ["profitx", "profity"]}, {"name": "Optimum strategy", "variables": ["intersection_points", "possible_points", "profits", "best_point", "best_x_float", "best_y_float", "best_profit_float", "best_x", "best_y", "best_profit", "best_lines", "line_names"]}, {"name": "Text strings", "variables": ["business_long", "business_short", "business", "resource_1", "resource_1_units", "resource_2", "resource_2_units", "product_1", "product_1s", "product_2", "product_2s"]}], "type": "question", "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}