// Numbas version: exam_results_page_options
{"name": "Andrew's copy of Inventory analysis: constant demand", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [{"name": "Names", "variables": ["company_names", "company", "product_data", "chosen_product", "product", "products", "unit", "units"]}, {"name": "Costs", "variables": ["demand", "labour", "clean", "clerical", "order_cost", "price", "holding_rate", "holding_cost"]}, {"name": "Answers", "variables": ["eoq", "minimum_cost"]}], "statement": "<p>The demand {company} receives for its {products} is $d = \\var{demand}$ {units} per year and is fairly constant throughout the year.</p>\n<p>The {product} is valued at $<strong>{price} per {unit}</strong> and is produced in batches. Each production run incurs the following costs:</p>\n<ul>\n<li><strong>${labour}</strong> for <g class=\"gr_ gr_9 gr-alert gr_spell gr_run_anim ContextualSpelling multiReplace\" id=\"9\" data-gr-id=\"9\">labour</g></li>\n<li><strong>${clean}</strong> to clean&nbsp;tools</li>\n<li><strong>${clerical}</strong> in clerical costs</li>\n</ul>\n<p>The costs of self-insurance and loss of investment income for money tied&nbsp;up in stock are rated at <strong>{holding_rate*100}%</strong>.</p>", "advice": "<h4>a)</h4>\n<p>The set-up cost for each batch is the sum of the labour, cleaning, and clerical costs:</p>\n<p>\\[ \\simplify[]{{labour} + {clean} + {clerical}} = \\var{order_cost} \\]</p>\n<p>The annual holding cost per {unit} is the product of the&nbsp;price per {unit} of {products} and the rated holding cost. That is,</p>\n<p>\\[ \\simplify[]{{price}*{holding_rate}} = \\var{holding_cost} \\]</p>\n<h4>b)</h4>\n<p>The economic order quantity is given by</p>\n<p>\\[ \\mathrm{EOQ} = \\sqrt{\\frac{2ad}{h}} \\]</p>\n<p>where $a = \\var{order_cost}$ is the set-up cost of each order, $d = \\var{demand}$ is the annual demand, and $h = \\var{holding_cost}$ is the annual holding cost per {unit}.</p>\n<p>Using the values calculated above, we have:</p>\n<p>\\[ \\mathrm{EOQ} = \\simplify[]{sqrt((2*{order_cost}*{demand})/{holding_cost})} = \\var{round(eoq)} \\, \\var{units} \\text{ (to the nearest }\\var{unit}\\text{)} \\]</p>\n<h4>c)</h4>\n<p>The minimum cost per year is given by&nbsp;</p>\n<p>\\[ \\sqrt{2adh} = &pound;\\var{precround(minimum_cost,2)} \\]</p>", "name": "Andrew's copy of Inventory analysis: constant demand", "ungrouped_variables": [], "parts": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>Set-up cost for each batch: <strong>$</strong>[[0]]</p>\n<p>Annual holding cost per {unit}: <strong>$</strong>[[1]]</p>", "variableReplacements": [], "scripts": {}, "showFeedbackIcon": true, "gaps": [{"precisionPartialCredit": 0, "showPrecisionHint": false, "showFeedbackIcon": true, "maxValue": "order_cost", "strictPrecision": false, "precisionType": "dp", "marks": 1, "minValue": "order_cost", "precision": "2", "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "variableReplacements": [], "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "type": "numberentry"}, {"precisionPartialCredit": 0, "showPrecisionHint": false, "showFeedbackIcon": true, "maxValue": "holding_cost", "strictPrecision": false, "precisionType": "dp", "marks": 1, "minValue": "holding_cost", "precision": "2", "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "variableReplacements": [], "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "type": "numberentry"}], "marks": 0, "type": "gapfill", "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "prompt": "<p>How much {product} should {company} produce&nbsp;in each batch? Round your answer to the nearest {unit}.</p>\n<p>[[0]] {units}</p>", "variableReplacements": [], "scripts": {}, "showFeedbackIcon": true, "gaps": [{"precisionPartialCredit": 0, "showPrecisionHint": false, "showFeedbackIcon": true, "maxValue": "eoq", "strictPrecision": false, "precisionType": "dp", "marks": 1, "minValue": "eoq", "precision": 0, "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "variableReplacements": [], "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "type": "numberentry"}], "marks": 0, "type": "gapfill", "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "prompt": "<p>What is {company}'s minimum cost per year? Round your answer to the nearest penny.</p>\n<p><strong>$</strong>[[0]]</p>", "variableReplacements": [], "scripts": {}, "showFeedbackIcon": true, "gaps": [{"precisionPartialCredit": 0, "showPrecisionHint": false, "showFeedbackIcon": true, "maxValue": "minimum_cost", "strictPrecision": false, "precisionType": "dp", "marks": 1, "minValue": "minimum_cost", "precision": "2", "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "variableReplacements": [{"must_go_first": false, "part": "p1g0", "variable": "eoq"}], "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "type": "numberentry"}], "marks": 0, "type": "gapfill", "showCorrectAnswer": true}], "tags": [], "variablesTest": {"condition": "", "maxRuns": 100}, "functions": {}, "variables": {"clean": {"description": "", "name": "clean", "templateType": "anything", "group": "Costs", "definition": "random(1..5)"}, "demand": {"description": "", "name": "demand", "templateType": "anything", "group": "Costs", "definition": "random(800..2500#50)"}, "units": {"description": "", "name": "units", "templateType": "anything", "group": "Names", "definition": "chosen_product[3]"}, "products": {"description": "", "name": "products", "templateType": "anything", "group": "Names", "definition": "chosen_product[1]"}, "labour": {"description": "", "name": "labour", "templateType": "anything", "group": "Costs", "definition": "random(4..7)"}, "chosen_product": {"description": "", "name": "chosen_product", "templateType": "anything", "group": "Names", "definition": "random(product_data)"}, "company": {"description": "", "name": "company", "templateType": "anything", "group": "Names", "definition": "random(company_names)"}, "holding_cost": {"description": "", "name": "holding_cost", "templateType": "anything", "group": "Costs", "definition": "holding_rate*price"}, "clerical": {"description": "", "name": "clerical", "templateType": "anything", "group": "Costs", "definition": "random(1..3)"}, "price": {"description": "", "name": "price", "templateType": "anything", "group": "Costs", "definition": "random(4..12)"}, "eoq": {"description": "", "name": "eoq", "templateType": "anything", "group": "Answers", "definition": "sqrt((2*order_cost*demand)/holding_cost)"}, "holding_rate": {"description": "", "name": "holding_rate", "templateType": "anything", "group": "Costs", "definition": "random(0.05..0.3#0.01)"}, "product": {"description": "", "name": "product", "templateType": "anything", "group": "Names", "definition": "chosen_product[0]"}, "company_names": {"description": "", "name": "company_names", "templateType": "list of strings", "group": "Names", "definition": "[ \"ProdCo\", \"Amalgamated Things, Inc.\", \"Barker & Sons\" ]"}, "minimum_cost": {"description": "", "name": "minimum_cost", "templateType": "anything", "group": "Answers", "definition": "order_cost*demand/eoq + holding_cost/2 * eoq"}, "unit": {"description": "", "name": "unit", "templateType": "anything", "group": "Names", "definition": "chosen_product[2]"}, "order_cost": {"description": "", "name": "order_cost", "templateType": "anything", "group": "Costs", "definition": "labour+clean+clerical"}, "product_data": {"description": "", "name": "product_data", "templateType": "anything", "group": "Names", "definition": "[\n  [\"dog tiara\",\"dog tiaras\",\"unit\",\"units\"],\n  [\"diesel\",\"diesel\",\"gallon\",\"gallons\"],\n  [\"stinky cheese\",\"stinky cheese\",\"kg\",\"kg\"]\n]"}}, "preamble": {"css": "", "js": ""}, "extensions": [], "metadata": {"description": "<p>Given constant demand for a product, calculate the economic order quantity, and the minimum cost per year.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {}, "type": "question", "contributors": [{"name": "Andrew Dunbar", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/770/"}]}]}], "contributors": [{"name": "Andrew Dunbar", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/770/"}]}