// Numbas version: finer_feedback_settings {"name": "Semester test 2 - Part B", "metadata": {"description": "", "licence": "All rights reserved"}, "duration": 4500, "percentPass": 0, "showQuestionGroupNames": true, "showstudentname": true, "question_groups": [{"name": "Question 1", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questions": [{"name": "Apply regression model to forecast trip productions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christo Venter", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4933/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "
The following trip production model is available:
\n\n
ti = 1.06 + 0.52*X1i + 0.21*X2i – 0.46*X3i
\n\n
where
\n\n
ti = trips produced (all purposes) per household per day, for household i
\nX1i = household size
\nX2i = number of cars per household
\nX3i = number of unemployed adults in household
", "advice": "", "rulesets": {}, "variables": {"A": {"name": "A", "group": "Inputs", "definition": "random(2,3,4)", "description": "no of adults
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", "templateType": "anything"}, "t": {"name": "t", "group": "Answers", "definition": "1.06+0.52*(A+C)+0.21*(1)-0.46*(B)", "description": "trip rate per household
", "templateType": "anything"}, "EE": {"name": "EE", "group": "Inputs", "definition": "random(800..1800)", "description": "no of car-owning hhs
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", "templateType": "anything"}, "J": {"name": "J", "group": "Inputs", "definition": "random(400..2000)", "description": "no of non-car hh
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", "templateType": "anything"}, "L": {"name": "L", "group": "Inputs", "definition": "int(K*random(0.2..0.7#0.1))", "description": "no of non-car unemployed
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", "templateType": "anything"}, "TNC": {"name": "TNC", "group": "Answers", "definition": "int(1.06*(J) + 0.52*(K) - 0.46*(L))", "description": "total trips by non-car hhs
", "templateType": "anything"}, "TT": {"name": "TT", "group": "Answers", "definition": "TCO+TNC", "description": "total trips all hhs
", "templateType": "anything"}, "N": {"name": "N", "group": "Inputs", "definition": "random(5 .. 20#1)", "description": "% increase in unemployed people
", "templateType": "randrange"}, "M": {"name": "M", "group": "Inputs", "definition": "N + random(5..15)", "description": "% of car-owners selling cars
", "templateType": "anything"}, "E1": {"name": "E1", "group": "Ungrouped variables", "definition": "int(EE*(100-M)/100)", "description": "new EE (no of car-own hh)
", "templateType": "anything"}, "HplusL1": {"name": "HplusL1", "group": "Ungrouped variables", "definition": "int((H+L)*(1+N/100))", "description": "new total no of unemployed
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", "minValue": "0.95*t", "maxValue": "1.05*t", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": "100", "precisionMessage": "You have not given your answer to two decimals.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "In a zone, there are two groups of households, car-owning and non-car owning households.
\nGroup | \nNumber of households | \nNumber of people | \nNumber of unemployed | \n
Car-owning | \n{EE} | \n{F} | \n{H} | \n
Non-car owning | \n{J} | \n{K} | \n{L} | \n
Every car-owning household owns only one car. Estimate the total daily number of trips produced by car-owning households.
", "minValue": "0.95*TCO", "maxValue": "1.05*TCO", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "5", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "Estimate the total number of trips produced by non-car owning households.
", "minValue": "0.95*TNC", "maxValue": "1.05*TNC", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [{"variable": "TCO", "part": "p1", "must_go_first": true}, {"variable": "TNC", "part": "p2", "must_go_first": true}], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": "2", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "What is the total number of trips produced in the zone?
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", "minValue": "0.95*deltaT", "maxValue": "1.05*deltaT", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "type": "question"}]}, {"name": "Question 2", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questions": [{"name": "Supply curves and average cost - conveyor belt vs trucks", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christo Venter", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4933/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "Moria mine plans to produce coal for a nearby Eskom power station. The distance between the two is {D} kilometers. The mine has two options to transport coal to the power station: they can construct a conveyor belt system, or contract with trucking companies who charge them per tonne-kilometer transported. Each transport option has a physical capacity due to the size of the infrastructure. There is some uncertainty about the volume of coal the power station will need.
\nThe details for the two alternatives are:
\nConveyor belt option
\n Fixed (capital) cost (annualised) R{Ccost_b} per year
Operating cost R{Ocost_b} per tonne-km
Capacity {Cap_b} tonnes per year
Truck option
\n Operating cost R{Ocost_t} per tonne-km
Capacity {Cap_t} tonnes per year
distance
", "templateType": "randrange"}, "Ccost_b": {"name": "Ccost_b", "group": "Inputs", "definition": "D*425000", "description": "Capital cost - belt
", "templateType": "anything"}, "Ocost_b": {"name": "Ocost_b", "group": "Inputs", "definition": "random(0.80..1.50#0.01)", "description": "Op cost per t.km - belt
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", "templateType": "anything"}, "Cap_b": {"name": "Cap_b", "group": "Inputs", "definition": "int(CriticalVolume*1.2/1000)*1000", "description": "Annual Capacity - belt
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", "templateType": "anything"}, "CriticalVolume": {"name": "CriticalVolume", "group": "Ungrouped variables", "definition": "int(Ccost_b / (D*(Ocost_t - Ocost_b)))", "description": "Critical volume (where avg cost_b = avg cost_t)
", "templateType": "anything"}, "Vol_low": {"name": "Vol_low", "group": "Inputs", "definition": "int(CriticalVolume*0.75/1000)*1000", "description": "Volume (Low volume scenario)
", "templateType": "anything"}, "Vol_hi": {"name": "Vol_hi", "group": "Inputs", "definition": "int(CriticalVolume*1.3/1000)*1000", "description": "Volume (High volume scenario)
", "templateType": "anything"}, "Acost_b": {"name": "Acost_b", "group": "Answers", "definition": "precround(Ccost_b / Vol_low + Ocost_b * D,2)", "description": "Avg cost - belt at low volume scenario (R/t)
", "templateType": "anything"}, "Acost_t": {"name": "Acost_t", "group": "Answers", "definition": "precround(Ocost_t*D,2)", "description": "Avg cost trucks (all volumes) (R/t)
", "templateType": "anything"}, "XAcost_b1": {"name": "XAcost_b1", "group": "Answers", "definition": "precround(((Ccost_b + Ocost_b * D * Cap_b)/ Vol_low),2)", "description": "Wrong calc for avg cost - use capacity instead of volume
", "templateType": "anything"}, "XAcost_b2": {"name": "XAcost_b2", "group": "Answers", "definition": "precround(((Ccost_b + Ocost_b * D * Vol_low)/ Cap_b),2)", "description": "Wrong calc for avg cost - use capacity instead of volume
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", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["CriticalVolume"], "variable_groups": [{"name": "Inputs", "variables": ["D", "Ccost_b", "Ocost_b", "Ocost_t", "Cap_b", "Cap_t", "Vol_low", "Vol_hi"]}, {"name": "Answers", "variables": ["Acost_b", "Acost_t", "XAcost_b1", "XAcost_b2", "XAcost_t1", "XAcost_t2"]}], "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": "Calculate the expected average (unit) cost for each option, in Rands per tonne of coal transported, and plot the values on a graph on your answer sheet. Use two scenarios: low volume ({Vol_low} tonnes per year), and high volume ({Vol_hi} tonnes per year).
\nFor the low volume scenario, what is the average cost for the conveyor belt option?
\nR[[0]] per tonne
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\nR[[0]] per tonne
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\nR[[0]] per tonne
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"}}, "feedback": {"showactualmark": false, "showtotalmark": true, "showanswerstate": false, "allowrevealanswer": false, "advicethreshold": 0, "intro": "Please remember to submit each answer.
\nPlease exit the exam when you have completed all questions.
\nRemember to submit photos or scans of your work on a sheet of paper (showing the answers) immediately after exiting this test.
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