ENG2031 Mathematical Modelling – Instructions for Assignment
Available: Tuesday 28th March 2023. Submission: 23:59 on Monday 24th April 2023.
You should already have submitted four worksheets on the various problems discussed in teaching weeks
4-8 in Semester 2.
Satisfactory attendance means submission of at least three out of four worksheets, and attending all but
two out of all those classes where ID scans operated (could be up to eleven). If you have good reasons for
missing more than one worksheet and/or more than two classes, then please submit a PEC form with
evidence etc. The Assignment mark will be scaled as follows:
Final mark = Assignment mark (%) x Attendance (%).
Attendance = 50% + (worksheets out of 3) x 20% + (classes out of N-2) x 30%.
Thus, if only two worksheets were submitted (2/3 x 20%) and four classes missed out of eleven (7/9 x 30%),
the final mark will be multiplied by 50+17+23=90%, and an assignment mark of 60% will be scaled to 54%.
For the principal marked assignment, you should write up one of these exercises as a full report, following
the instructions below. One has been allocated to you – listed at the end of this document.
General instructions
- Submit your work via Canvas as a single file (PDF preferred, or JPG, JPEG, PNG, DOC), using your
surname as the filename, and check it’s readable on-screen! Best to put your name at the top of
the report also. (Don’t leave this until the final evening in case of IT problems.)
- Maximum of eight pages.
- Properly set-out, with headings: Description of problem (including diagram); Data/parameters,
Assumptions, Simplifications; Equations and solution for basic problem; Interpretation/Application
of solution; Comments, including which simplifications should be re-examined (including when
applied to other situations); Final conclusions about effectiveness of modelling.
- Few marks will be awarded for work that was covered in class, i.e. basic model for output
optimisation, and basic model for car-parking
Specific instructions for the case-studies
Crop production (output optimization)
- You should give a formula for the optimum length of life in terms of the chosen parameters a, b, c,
d, and check that this gives sensible results for some simple choices.
- Also find the average yield over that lifetime, and the output value at that point.
- Using a spreadsheet or otherwise, show a range of results for different choices of a, b, c (with d=25
fixed). Comment on how the results depend on each parameter – is one more critical than the
others?
- How would you turn your results into a practical piece of advice? Consider the assumptions and
simplifications that have been made and how those will affect your conclusions.
- How would the advice be different for (a) a single unit or small number of units, (b) a large area or
large number of units?
- Calculate new results using a different shape for the final section of the output curve (a quadratic
or two straight lines, or both – you might need to solve the final equation numerically). How do
your conclusions change?
- Comment on the general application of this approach to the lifetime productivity of various
economic units, also maintenance schedules, etc.
Car-parking (design of manoeuvring space)
- Explain why we can look at the problem of driving out instead of driving in.
- Give a comprehensive table of Assumptions and Simplifications for the Car, the Driver and the
Environment. Indicate which Simplifications are likely to be most critical.
- For the initial simplified analysis, use real data and check your results are credible, also put them
into a practical form. Also look at a range of other vehicles (smaller, larger, bus, etc.)
- How would your results change if the obstruction were a kerb instead of a wall or car?
- What simple modifications can you make and how significant are they?
- After clearing the car/kerb in front, there are two principal sequences to move to a parallel
position. Produce careful, labelled diagrams and indicate how you might calculate the final position.
- How would you produce practical advice from these results, not only for parking but also for a
range of other manoeuvring problems?
Concluding remarks
The aim of this part of ENG2031 was to get you thinking about how a real engineering problem is
formulated, starting with a brief from a client or colleague, who may be quite unclear about what they
want or need. Stages include:
- Understanding and defining the problem carefully, including how the solution is to be applied and
by whom;
- Obtaining all necessary information and data;
- Stating explicitly all Assumptions – aspects that can be completely included or excluded;
- Stating explicitly all Simplifications – deliberate changes to the problem to make it possible to solve,
or to make it clearer to understand or apply, but where some might need to be revisited later;
- Being clear about techniques used and how reliable they are;
- Checking that solutions are both correctly obtained and realistic in practice (by using previous
results or simplified values etc.);
- Revisiting major simplifications, identifying critical dependencies;
- If your work is unfinished, make clear where you have reached and what remains;
- Writing clear conclusions, with limitations etc. and including advice on any further work you’d
advise and/or which you think is feasible.
Your report should aim to describe the problem, method and results in line with this general ‘philosophy’.
The classes and your work on the five examples should help you to do this.
John Appleby, March 2023
Allocation of case-studies – submit only the allocated problem as a single file (PDF, JPG, JPEG, PNG, DOC)
ID Case ID Case ID Case ID Case
170475387 Crops 200814346 Cars 210096064 Crops 210229721 Cars
180135341 Cars 200821676 Crops 210099191 Cars 210238479 Crops
190012289 Crops 200831228 Cars 210101232 Crops 210240564 Cars
190154534 Cars 200832627 Crops 210101922 Cars 210240715 Crops
190193407 Crops 200839811 Cars 210103188 Crops 210241952 Cars
190272997 Cars 200848341 Crops 210114494 Cars 210242029 Crops
190356149 Crops 200874993 Cars 210115871 Crops 210249051 Cars
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200059165 Crops 200913959 Cars 210124529 Crops 210255373 Cars
200071031 Cars 200934334 Crops 210124873 Cars 210255535 Crops
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