topic 5 - linear programming

8/13/2019 Topic 5 - Linear Programming

1/5

STAGE 2 MATHEMATICS PATHWAYSFOLIO TASK

Linear programming Charity or!

Topi"# Optimi$ation

S%&topi"$ 'rom the Stage 2 Mathemati"a( App(i"ation$ S%&)e"t O%t(ine#

*+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 beused

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 Assessment Design Criteria Capabilities

1. emonstrate an understandingof mathematical concepts andrelationships.

!. "dentify, collect, and organisemathematical informationrelevant to investigating andfinding solutions toquestions/problems.

#. $ecognise and apply themathematical techniquesneeded when analysing andfinding a solution to aquestion/problem in context.

%. &a'e informed use ofelectronic technology to aidand enhance understanding.

(. "nterpret results, drawconclusions, and reflect on thereasonableness of these in thecontext of thequestion/problem.

). *ommunicate mathematicalideas and reasoning usingappropriate language andrepresentations.

Mathemati"a( Kno(e,ge an, S!i(($ an, TheirApp(i"ation

+he specific features are as follows:

&A1 nowledge of content and understandingof mathematical concepts and relationships.

&A! se of mathematical algorithms andtechniques implemented electronically whereappropriate0 to find solutions to routine andcomplex questions.

&A# Application of 'nowledge and s'ills toanswer questions in applied contexts.

Mathemati"a( Mo,e((ing an, Pro&(em-$o(.ing


&&1 Application of mathematical models.

&&! evelopment of mathematical results forproblems set in applied contexts.

& "nterpretation of the mathematical results inthe context of the problem.

&&% nderstanding of the reasonableness andpossible limitations of the interpreted results, andrecognition of assumptions made..

Comm%ni"ation o' Mathemati"a( In'ormation


*&"1 *ommunication of mathematical ideas andreasoning to develop logical arguments.

*&"! se of appropriate mathematical notation,

representations, and terminology.

*ommunication

*iti2enship

ersonalevelopment

3or'

4earning

age 1 of ( tage ! &athematics athways 5ptimisation tas'$ef: A!6#7!! revised 8ovember !61#0

9 A* ;oard of outh Australia !61!


2/5

PE/FO/MA0CE STA01A/1S FO/ STAGE 2 MATHEMATICS PATHWAYS

Mathemati"a( Kno(e,ge an,S!i(($ an, Their App(i"ation


Comm%ni"ation o'Mathemati"a( In'ormation

A *omprehensive 'nowledge ofcontent and understanding ofconcepts and relationships.

Appropriate selection and use ofmathematical algorithms andtechniques implementedelectronically where appropriate0 tofind efficient solutions to complexquestions.


3/5

Mathemati"a( Kno(e,ge an,S!i(($ an, Their App(i"ation


Comm%ni"ation o'Mathemati"a( In'ormation

solutions to routine questions.

Attempted application of 'nowledgeand s'ills to answer questions setin applied contexts, with limitedeffectiveness.

mathematical results in the context of the problem.

4imited awareness of the reasonableness andpossible limitations of the results.

terminology, and with limitedaccuracy.

age # of ( tage ! &athematics athways 5ptimisation tas'$ef: A!6#7!! revised 8ovember !61#09 A* ;oard of outh Australia !61!


4/5

STAGE 2 MATHEMATICS PATHWAYSFOLIO TASK

Linear programming Charity Wor!

Intro,%"tion

+he purpose of this investigation is to allow you to demonstrate your 'nowledge and ability to

accurately apply the mathematical concepts and processes of 4inear programming to a fundraising scenario.

1e$"ription o' a$$e$$ment

+his folio tas's loo's at investigating the amount of money that may be raised through a home helpfundraising day to support a charity. "nformation given will lead to a set of constraints and anob>ective function. 3ith the use of appropriate technology you will graph the constraints andanalyse the feasible region to determine the optimal solution/s.

As a class, you decided to as' family and friends to support you to raise money for a charityorganisation. ?ou as'ed them to volunteer their time to a home help day in which they could offer

to do housewor', gardening or general maintenance. +he class received the following donations oftime for the three categories of home help:

!6 hours of housewor'

%% hours of gardening

!7 hours of general maintenance.

+he class have decided to offer two different pac'ages of home help to the community.

ac'age 1 has ! hours of housewor', % hours of gardening and ! hours of generalmaintenance. +he class have decided to sell this pac'age for @1#6.

ac'age ! includes 1 hour of housewor', # hours of gardening and ! hours of generalmaintenance. +he class have decided to sell this pac'age for @116.

Mathemati"a( In.e$tigation$

3+ se all of the information provided above to determine the combination of pac'ages to besold to achieve the greatest optimal0 profit for the classes fundraising efforts.

2+ "nvestigate at least two variations to this original scenario. ?ou could consider: changes tothe price of the pac'ages variations to the time donated the amount of hours of each homehelp category that are included in each pac'age. Bor each variation investigated, provide ashort description of what the change is and how it may have come about to set the scene ofthe investigation.

4+ resent your findings in an investigative report as described on page 1. ?our analysis andconclusion 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.

age % of ( tage ! &athematics athways 5ptimisation tas'$ef: A!6#7!! revised 8ovember !61#0



5/5

This task has been reproduced with the kind permission of Annalisi Tsoukatos.

age ( of ( tage ! &athematics athways 5ptimisation tas'$ef: A!6#7!! revised 8ovember !61#0


topic 5 - linear programming

Documents