Topic 10 Practice - Solutions
:KLFKFRPSRXQGLVLQVROXEOHLQZDWHU"
$ FDOFLXPEURPLGH
& VLOYHUEURPLGH
% SRWDVVLXPEURPLGH
' VRGLXPEURPLGH
:KLFKEDULXPVDOWLVLQVROXEOHLQZDWHU"
$ %D&2 & %D&O2 % %D&O
' %D12 :KLFKFRPSRXQGEHFRPHVOHVVVROXEOHLQZDWHUDVWKH
WHPSHUDWXUHRIWKHVROXWLRQLVLQFUHDVHG"
$ +&O
& 1D&O
% .&O
' 1+ &O
$FFRUGLQJWR7DEOH)ZKLFKFRPSRXQGLVVROXEOHLQ
ZDWHU"
$ EDULXPSKRVSKDWH
& VLOYHULRGLGH
% FDOFLXPVXOIDWH
' VRGLXPSHUFKORUDWH
:KLFKFRPSRXQGLVOHDVWVROXEOHLQZDWHUDWƒ&"
$ .&O2 & 1D&O
% .12
' 1+ &O
$WURRPWHPSHUDWXUHWKHVROXELOLW\RIZKLFKVROXWHLQ
ZDWHUZRXOGEHPRVWDIIHFWHGE\DFKDQJHLQSUHVVXUH"
$ PHWKDQRO
& FDUERQGLR[LGH
% VXJDU
' VRGLXPQLWUDWH
%DVH\RXUDQVZHUWRWKHIROORZLQJTXHVWLRQRQ*LYHQWKH
GLDJUDPEHORZWKDWVKRZVFDUERQGLR[LGHLQDQ
HTXLOLEULXPV\VWHPDWDWHPSHUDWXUHRI.DQGD
SUHVVXUHRIDWP
$VWXGHQWDGGVVROLG.&OWRZDWHULQDIODVN7KHIODVNLV
VHDOHGZLWKDVWRSSHUDQGWKRURXJKO\VKDNHQXQWLOQR
PRUHVROLG.&OGLVVROYHV6RPHVROLG.&OLVVWLOOYLVLEOH
LQWKHIODVN7KHVROXWLRQLQWKHIODVNLV
$ VDWXUDWHGDQGLVDWHTXLOLEULXPZLWKWKHVROLG.&O
% VDWXUDWHGDQGLVQRWDWHTXLOLEULXPZLWKWKHVROLG
.&O
& XQVDWXUDWHGDQGLVDWHTXLOLEULXPZLWKWKHVROLG.&O
' XQVDWXUDWHGDQGLVQRWDWHTXLOLEULXPZLWKWKHVROLG
.&O
$VROXWHLVDGGHGWRZDWHUDQGDSRUWLRQRIWKHVROXWH
UHPDLQVXQGLVVROYHG:KHQHTXLOLEULXPEHWZHHQWKH
GLVVROYHGDQGXQGLVVROYHGVROXWHLVUHDFKHGWKHVROXWLRQ
PXVWEH
$ GLOXWH
& XQVDWXUDWHG
% VDWXUDWHG
' VXSHUVDWXUDWHG
:KHQJUDPVRI.&ODUHGLVVROYHGLQJUDPVRI
ZDWHUDWƒ&WKHUHVXOWLQJPL[WXUHFDQEHGHVFULEHGDV
$
%
&
'
KHWHURJHQHRXVDQGXQVDWXUDWHG
KHWHURJHQHRXVDQGVXSHUVDWXUDWHG
KRPRJHQHRXVDQGXQVDWXUDWHG
KRPRJHQHRXVDQGVXSHUVDWXUDWHG
$VROXWLRQFRQWDLQVJUDPVRI.12 GLVVROYHGLQ
JUDPVRIZDWHUDWƒ&+RZPXFKPRUH.12ZRXOG
KDYHWREHDGGHGWRPDNHLWDVDWXUDWHGVROXWLRQ"
$ J
% J
& J
' J
$0+&ODTVROXWLRQFRQWDLQVDWRWDORI
$
%
&
'
JUDPVRI+&OSHUOLWHURIZDWHU
JUDPVRI+&OSHUPROHRIVROXWLRQ
PROHVRI+&OSHUOLWHURIVROXWLRQ
PROHVRI+&OSHUPROHRIZDWHU
:KDWLVWKHWRWDOQXPEHURIPROHVRI1D&OVQHHGHGWR
PDNHOLWHUVRID01D&OVROXWLRQ"
:KLFKFKDQJHVPXVWLQFUHDVHWKHVROXELOLW\RIWKHFDUERQ
GLR[LGH"
$
%
&
'
LQFUHDVHSUHVVXUHDQGGHFUHDVHWHPSHUDWXUH
LQFUHDVHSUHVVXUHDQGLQFUHDVHWHPSHUDWXUH
GHFUHDVHSUHVVXUHDQGGHFUHDVHWHPSHUDWXUH
GHFUHDVHSUHVVXUHDQGLQFUHDVHWHPSHUDWXUH
$ PRO
& PRO
% PRO
' PRO
:KLFKXQLWFDQEHXVHGWRH[SUHVVWKHFRQFHQWUDWLRQRI
DVROXWLRQ"
$ /V
% -J
& SSP
' N3D
+RZPDQ\JUDPVRI1D&ODUHQHHGHGWREHGLVVROYHGLQ
ZDWHUWRPDNHJUDPRIDSSPVROXWLRQ"
$ î J
& î J
% î J
' î J
$VWXGHQWZDQWVWRSUHSDUHDOLWHUVROXWLRQRID
VSHFLILFPRODULW\7KHVWXGHQWGHWHUPLQHVWKDWWKHPDVV
RIWKHVROXWHQHHGVWREHJUDPV:KDWLVWKHSURSHU
SURFHGXUHWRIROORZ"
$ $GGJRIVROXWHWR/RIVROYHQW
% $GGJRIVROXWHWRP/RIVROYHQWWRPDNH
/RIVROXWLRQ
& $GGJRIVROYHQWWRJRIVROXWH
' $GGHQRXJKVROYHQWWRJRIVROXWHWRPDNH
/RIVROXWLRQ
&RPSDUHGWRWKHIUHH]LQJSRLQWDQGERLOLQJSRLQWRI
ZDWHUDWDWPRVSKHUHDVROXWLRQRIDVDOWDQGZDWHUDW
DWPRVSKHUHKDVD
$
%
&
'
ORZHUIUHH]LQJSRLQWDQGDORZHUERLOLQJSRLQW
ORZHUIUHH]LQJSRLQWDQGDKLJKHUERLOLQJSRLQW
KLJKHUIUHH]LQJSRLQWDQGDORZHUERLOLQJSRLQW
KLJKHUIUHH]LQJSRLQWDQGDKLJKHUERLOLQJSRLQW
:KLFKVROXWLRQKDVWKHORZHVWIUHH]LQJSRLQW"
$
%
&
'
JRI.,GLVVROYHGLQJRIZDWHU
JRI.,GLVVROYHGLQJRIZDWHU
JRI.,GLVVROYHGLQJRIZDWHU
JRI.,GLVVROYHGLQJRIZDWHU
&RPSDUHGWRD0DTXHRXVVROXWLRQRI1D&ODW
DWPRVSKHUHD0DTXHRXVVROXWLRQRI1D&ODW
DWPRVSKHUHKDVD
$
%
&
'
ORZHUERLOLQJSRLQWDQGDKLJKHUIUHH]LQJSRLQW
ORZHUERLOLQJSRLQWDQGDORZHUIUHH]LQJSRLQW
KLJKHUERLOLQJSRLQWDQGDKLJKHUIUHH]LQJSRLQW
KLJKHUERLOLQJSRLQWDQGDORZHUIUHH]LQJSRLQW
:KHQHWK\OHQHJO\FRODQDQWLIUHH]HLVDGGHGWRZDWHU
WKHERLOLQJSRLQWRIWKHZDWHU
$
%
&
'
GHFUHDVHVDQGWKHIUHH]LQJSRLQWGHFUHDVHV
GHFUHDVHVDQGWKHIUHH]LQJSRLQWLQFUHDVHV
LQFUHDVHVDQGWKHIUHH]LQJSRLQWGHFUHDVHV
LQFUHDVHVDQGWKHIUHH]LQJSRLQWLQFUHDVHV
$QVZHU.H\
7RSLF3UDFWLFH6ROXWLRQV
&
$
$
'
$
&
$
$
%
&
$
&
$
&
$
'
%
&
'
&