// 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

\n

X1i = household size

\n

X2i = number of cars per household

\n

X3i = number of unemployed adults in household

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no of adults

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No of unemployed

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no of children

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trip rate per household

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no of car-owning hhs

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no of car-owning people

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no of car-owning unemployed

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no of non-car hh

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no of non-car people

", "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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total trips by car-owning hhs

", "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

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total trips all hhs

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% increase in unemployed people

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% of car-owners selling cars

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new EE (no of car-own hh)

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new total no of unemployed

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decrease in total trips (positive)

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If a particular household had {A} adults of which {B} was unemployed, {C} children, and 1 car, estimate the daily number of trips it would generate.

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In a zone, there are two groups of households, car-owning and non-car owning households.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
GroupNumber of
households
Number of
people
Number of
unemployed
Car-owning{EE}{F}{H}
Non-car owning{J}{K}{L}
\n

Every car-owning household owns only one car. Estimate the total daily number of trips produced by car-owning households.

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Estimate the total number of trips produced by non-car owning households.

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What is the total number of trips produced in the zone?

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Poor economic conditions after lockdown cause {M}% of car-owning households in the zone to sell their car, and the number of unemployed people to increase by {N}%. By how many trips would the total productions decrease (assuming all other variables remain constant)?

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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. 

\n

The details for the two alternatives are:

\n

Conveyor 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

\n

Truck option

\n

  Operating cost                              R{Ocost_t} per tonne-km
  Capacity                                       {Cap_t} tonnes per year

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distance

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Capital cost - belt

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Op cost per t.km - belt

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Op cost per t.km - truck

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Annual Capacity - belt

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Annual Capacity - truck

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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)

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Wrong calc for avg cost - use capacity instead of volume

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Wrong calc for avg cost - use capacity instead of volume

", "templateType": "anything"}, "XAcost_t1": {"name": "XAcost_t1", "group": "Answers", "definition": "precround(((Ocost_t * D * Cap_t)/ Vol_low),2)", "description": "

Wrong calc for avg cost - use capacity instead of volume

", "templateType": "anything"}, "XAcost_t2": {"name": "XAcost_t2", "group": "Answers", "definition": "precround(((Ocost_t * D * Vol_low)/ Cap_t),2)", "description": "

Wrong calc for avg cost - use capacity instead of volume

", "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).

\n

For the low volume scenario, what is the average cost for the conveyor belt option?

\n

R[[0]] per tonne

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You used capacity instead of volume when calculating average cost

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You used capacity instead of volume when calculating average cost

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For the low volume scenario, what is the average cost for the trucking option?

\n

R[[0]] per tonne

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You used capacity instead of volume when calculating average cost

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You used capacity instead of volume when calculating average cost

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For the low volume scenario, which option should be selected (based on costs alone)?

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Which of the two options has the highest economies of scale?

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For the high volume scenario, what is the average cost for the trucking option?

\n

R[[0]] per tonne

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For the high volume scenario, which option should be selected?

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You have not attempted all questions.

"}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": false, "timeout": {"action": "warn", "message": "

Your exam session has expired

"}, "timedwarning": {"action": "warn", "message": "

Your exam session will expire in 5 minutes.

"}}, "feedback": {"showactualmark": false, "showtotalmark": true, "showanswerstate": false, "allowrevealanswer": false, "advicethreshold": 0, "intro": "

Please remember to submit each answer.

\n

Please exit the exam when you have completed all questions.

\n

Remember to submit photos or scans of your work on a sheet of paper (showing the answers) immediately after exiting this test.

", "reviewshowscore": true, "reviewshowfeedback": false, "reviewshowexpectedanswer": true, "reviewshowadvice": false, "feedbackmessages": [], "enterreviewmodeimmediately": false, "showexpectedanswerswhen": "never", "showpartfeedbackmessageswhen": "never", "showactualmarkwhen": "never", "showtotalmarkwhen": "always", "showanswerstatewhen": "inreview", "showadvicewhen": "never"}, "type": "exam", "contributors": [{"name": "Christo Venter", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4933/"}], "extensions": [], "custom_part_types": [], "resources": []}