STAGE 2 MATHEMATICS PATHWAYS
FOLIO TASK
Linear programming – Charity work
Topic:
Optimisation
Subtopics from the Stage 2 Mathematical Applications Subject Outline:
5.2 – Linear Programming
A completed investigation should include:
 an introduction that outlines the problem to be explored, including it significance, its features,
and the context
 the method required to find a solution, in terms of the mathematical model or strategy to be
used
 the appropriate application of the mathematical model or strategy, including
- the generation or collection of relevant data and/or information, with details of the process
of collection
- mathematical calculations and results, and appropriate representations
- the analysis and interpretation of results
- reference to the limitations of the original problem
 a statement of the results and conclusions in the context of the original problem
 appendices and a bibliography, as appropriate.
Learning Requirements
1.
2.
3.
4.
5.
6.
Assessment Design Criteria
Capabilities
Demonstrate an understanding
of mathematical concepts and
relationships.
Mathematical Knowledge and Skills and Their
Application
Communication
Identify, collect, and organise
mathematical information
relevant to investigating and
finding solutions to
questions/problems.

MKSA1 Knowledge of content and understanding
of mathematical concepts and relationships.

MKSA2 Use of mathematical algorithms and
techniques (implemented electronically where
appropriate) to find solutions to routine and
complex questions.
Recognise and apply the
mathematical techniques
needed when analysing and
finding a solution to a
question/problem in context.
Make informed use of
electronic technology to aid
and enhance understanding.
Interpret results, draw
conclusions, and reflect on the
reasonableness of these in the
context of the
question/problem.
Communicate mathematical
ideas and reasoning using
appropriate language and
representations.
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The specific features are as follows:

Citizenship
Personal
Development
Work
Learning
MKSA3 Application of knowledge and skills to
answer questions in applied contexts.
Mathematical Modelling and Problem-solving
The specific features are as follows:

MMP1 Application of mathematical models.

MMP2 Development of mathematical results for
problems set in applied contexts.

MMP3 Interpretation of the mathematical results in
the context of the problem.

MMP4 Understanding of the reasonableness and
possible limitations of the interpreted results, and
recognition of assumptions made..
Communication of Mathematical Information
The specific features are as follows:

CMI1 Communication of mathematical ideas and
reasoning to develop logical arguments.

CMI2 Use of appropriate mathematical notation,
representations, and terminology.
Stage 2 Mathematics Pathways Optimisation task
Ref: A203822 (revised February 2016)
© SACE Board of South Australia 2012
PERFORMANCE STANDARDS FOR STAGE 2 MATHEMATICS PATHWAYS
Mathematical Knowledge and
Skills and Their Application
A
Comprehensive knowledge of
content and understanding of
concepts and relationships.
Appropriate selection and use of
mathematical algorithms and
techniques (implemented
electronically where appropriate) to
find efficient solutions to complex
questions.
Highly effective and accurate
application of knowledge and skills
to answer questions set in applied
contexts.
B
Some depth of knowledge of
content and understanding of
concepts and relationships.
Use of mathematical algorithms
and techniques (implemented
electronically where appropriate) to
find some correct solutions to
complex questions.
Accurate application of knowledge
and skills to answer questions set
in applied contexts.
C
Generally competent knowledge of
content and understanding of
concepts and relationships.
Use of mathematical algorithms
and techniques (implemented
electronically where appropriate) to
find mostly correct solutions to
routine questions.
Generally accurate application of
knowledge and skills to answer
questions set in applied contexts.
D
Basic knowledge of content and
some understanding of concepts
and relationships.
Some use of mathematical
algorithms and techniques
(implemented electronically where
appropriate) to find some correct
solutions to routine questions.
Sometimes accurate application of
knowledge and skills to answer
questions set in applied contexts.
E
Limited knowledge of content.
Attempted use of mathematical
algorithms and techniques
(implemented electronically where
appropriate) to find limited correct
solutions to routine questions.
Attempted application of knowledge
and skills to answer questions set
in applied contexts, with limited
effectiveness.
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Mathematical Modelling and Problemsolving
Development and effective application of
mathematical models.
Complete, concise, and accurate solutions to
mathematical problems set in applied contexts.
Concise interpretation of the mathematical results
in the context of the problem.
Communication of
Mathematical Information
Highly effective communication of
mathematical ideas and reasoning
to develop logical arguments.
Proficient and accurate use of
appropriate notation,
representations, and terminology.
In-depth understanding of the reasonableness and
possible limitations of the interpreted results, and
recognition of assumptions made.
Attempted development and appropriate application
of mathematical models.
Mostly accurate and complete solutions to
mathematical problems set in applied contexts.
Complete interpretation of the mathematical results
in the context of the problem.
Effective communication of
mathematical ideas and reasoning
to develop mostly logical
arguments.
Mostly accurate use of
appropriate notation,
representations, and terminology.
Some depth of understanding of the
reasonableness and possible limitations of the
interpreted results, and recognition of assumptions
made.
Appropriate application of mathematical models.
Some accurate and generally complete solutions to
mathematical problems set in applied contexts.
Generally appropriate interpretation of the
mathematical results in the context of the problem.
Some understanding of the reasonableness and
possible limitations of the interpreted results, and
some recognition of assumptions made.
Application of a mathematical model, with partial
effectiveness.
Partly accurate and generally incomplete solutions
to mathematical problems set in applied contexts.
Attempted interpretation of the mathematical results
in the context of the problem.
Appropriate communication of
mathematical ideas and reasoning
to develop some logical
arguments.
Use of generally appropriate
notation, representations, and
terminology, with some
inaccuracies.
Some appropriate communication
of mathematical ideas and
reasoning.
Some attempt to use appropriate
notation, representations, and
terminology, with occasional
accuracy.
Some awareness of the reasonableness and
possible limitations of the interpreted results.
Attempted application of a basic mathematical
model.
Limited accuracy in solutions to one or more
mathematical problems set in applied contexts.
Limited attempt at interpretation of the
mathematical results in the context of the problem.
Attempted communication of
emerging mathematical ideas and
reasoning.
Limited attempt to use appropriate
notation, representations, or
terminology, and with limited
accuracy.
Limited awareness of the reasonableness and
possible limitations of the results.
Stage 2 Mathematics Pathways Optimisation task
Ref: A203822 (revised February 2016)
© SACE Board of South Australia 2012
STAGE 2 MATHEMATICS PATHWAYS
FOLIO TASK
Linear programming – Charity Work
Introduction
The purpose of this investigation is to allow you to demonstrate your knowledge and ability to
accurately apply the mathematical concepts and processes of Linear programming to a fund
raising scenario.
Description of assessment
This folio tasks looks at investigating the amount of money that may be raised through a home help
fundraising day to support a charity. Information given will lead to a set of constraints and an
objective function. With the use of appropriate technology you will graph the constraints and
analyse the feasible region to determine the optimal solution/s.
As a class, you decided to ask family and friends to support you to raise money for a charity
organisation. You asked them to volunteer their time to a home help day in which they could offer
to do housework, gardening or general maintenance. The class received the following donations of
time for the three categories of home help:

20 hours of housework

44 hours of gardening

28 hours of general maintenance.
The class have decided to offer two different packages of home help to the community.

Package 1 has 2 hours of housework, 4 hours of gardening and 2 hours of general
maintenance. The class have decided to sell this package for $130.

Package 2 includes 1 hour of housework, 3 hours of gardening and 2 hours of general
maintenance. The class have decided to sell this package for $110.
Mathematical Investigations
1.
Use all of the information provided above to determine the combination of packages to be
sold to achieve the greatest (optimal) profit for the classes fundraising efforts.
2.
Investigate at least two variations to this original scenario. You could consider: changes to
the price of the packages; variations to the time donated; the amount of hours of each home
help category that are included in each package. For each variation investigated, provide a
short description of what the change is and how it may have come about to set the scene of
the investigation.
3.
Present your findings in an investigative report as described on page 1. Your analysis and
conclusion should include:

a comparison of the different scenarios investigated

what is the optimal solution

the assumptions that were made in your calculations and therefore the
reasonableness of the optimal solution

the limitations of the model used.
This task has been reproduced with the kind permission of Annalisi Tsoukatos.
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Stage 2 Mathematics Pathways Optimisation task
Ref: A203822 (revised February 2016)
© SACE Board of South Australia 2012