Pearson Edexcel Level 3 GCE Further Mathematics Advanced Subsidiary Further Mathematics options 28

Pearson Edexcel Level 3 GCE T T T T




PaperTref
erence 8FM0/28
FurtherMathematics T




Advanced Subsidiary Further T T


Mathematics options28: Deci
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sion Mathematics 2 (Part of opt
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ion K only) T T




YouTmustThave:TMathematicalTFormulaeTandTStatisticalTTablesT(Green),Tc
alculator,TD2TAnswerTBookT(enclosed)


CandidatesTmayTuseTanyTcalculatorTallowedTbyTPearsonTregulations.TC
alculatorsTmustTnotThaveTtheTfacilityTforTsymbolicTalgebraTmanipulatio
n,TdifferentiationTandTintegration,TorThaveTretrievableTmathematical
TformulaeTstoredTinTthem.



Instructions
• Use black ink or ball-point pen.
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• Ifinpencil is used for diagrams/sketches/graphs it must be dark (HB or B).Fill
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• mbertheandboxes
T at the top of the answer book with your name, centre nu
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candidate number. T
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• Answer all questions and ensure that your answers to parts of questions arecl
early labelled. T
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• Answer the questions in the Answer Book provided
– there may be more space than you need.
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• You should show sufficient working to make your methods clear.Answers
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without working may not gain full credit. T
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• Inexact
tated.
answers should be given to three significant figures unless otherwises
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• Do not return the question paper with the D2 Answer Book.
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Information
• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
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• marks for eachforquestion
total mark this part of the examination is 40. There are 4 questions.The
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• – use this as a guide as to how
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are shown in brackets
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much time to spend on each question.
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Advice
• Read each question carefully before you start to answer it.
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• Check
Try to answer every question.
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•• Good luck
your answers if you have time at the end.
with your examination.
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TurnTover


P66795A
©2021T PearsonT EducationT Ltd.

1/1/1/1/1/

, WriteTyourTanswersTinTtheTanswerTbookTprovided.

1. FiveTworkers,TA,TB,TC,TDTandTE,TareTavailableTtoTcompleteTfourTtasks,TP,TQ,TRTandTS.

EachTtaskTmustT beTassignedT toTexactlyToneT workerTandT eachTworkerTcanTdoTatT mostToneTtask.TWork

erTBT cannotT beT assignedTtoT taskT R.

TheTamount,TinTpounds,TthatTeachTworkerTwillTearnTifTtheyTareTassignedTtoTeachTtaskTisTshownTinTtheT
tableTbelow.

P Q R S
A 55 56 58 57
B 60 61 – 64
C 59 60 62 63
D 64 66 71 69
E 65 68 72 66

TheTHungarianTalgorithmTisTtoTbeTusedTtoTfindTtheTmaximumTtotalTamountTthatTcanTbeTearnedTbyTthe
fiveTworkers.
T




(a) ExplainThowTtheTtableTshouldTbeTmodifiedTtoTallowTtheTHungarianTalgorithmTtoTbeTused,TgivingT
reasonsTforT yourT answer.
(2)

(b) ReducingT rowsT first,T useT theT HungarianT algorithmT toT obtainT theT maximumT possibleT totalT
earnings.TYouTshouldTexplainThowTanyTinitialTrowTandTcolumnTreductionsTwereTmadeTandThowT
youTdeterminedTifT theT tableTwasToptimalTatT eachTstage.
(7)

(TotalTforTQuestionT1TisT9Tmarks)




P66795A 2

, 2.

A 31 30 G

14 0 25
13 8 25
60
21 C 17
66 T
17 19 35 5
19 32
47 41 36
S 37
D 20TTT 13 F
64
28 19
24 28 74
2 1 15
24 15 11


B 32 22 E 56 49 H

FigureT1

FigureT1TshowsTaTcapacitated,TdirectedTnetwork.TTheTnumberTonTeachTarcTrepresentsTtheTcapacityTofT
thatTarc.TTheT numbersT inTcirclesTrepresentT anT initialTflow.

(a) StateTtheTvalueTofTtheTinitialTflow.
(1)

(b) ObtainTtheTcapacityTofTtheTcutTthatTpassesTthroughTtheTarcsTAG,TCG,TGF,TFT,TFHTandTEH.
(1)

(c) CompleteT theT initialisationT ofT theT labellingT procedureT onT DiagramT 1T inT theT answerT bookT byT
enteringTvaluesT alongT SD,TBD,T BET andT GF.
(2)

(d) UseT theT labellingT procedureT toT findT aT maximumT flowT throughT theT network.TYouT mustT listT eachT
flow-augmentingTrouteT youT use,TtogetherTwithTitsTflow.
(3)

(e) UseTtheT answerTtoT partT(d)T toT addTaT maximumTflowT patternTtoTDiagramT2TinT theTanswerT book.
(1)

(f) ProveTthatT yourTanswerT toTpartT (e)TisT optimal.
(3)

(TotalTforTQuestionT2TisT11Tmarks)




P66795A 3 TurnTover