chapter # 10 - engineering economy, 7 th editionleland blank and anthony tarquin
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7/23/2019 Chapter # 10 - Engineering Economy, 7 th editionLeland Blank and Anthony Tarquin
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Tmauzimgt zm ogj.me.dhc|zor |rmbaontOg`igoorig` Odmgmny! 0zh ojizimg
Aoacgj Bacgf cgj Cgzhmgy Zcrsuig
Dhc|zor 3<
\rmkodz Eigcgdig` cgj Gmg.odmgmnid Czzribuzot
3<'3 Ritf — Zho hi`hor zho ritf! zho hi`hor zho NCRRIgotznogz M||mrzugizy — NCRR ncy bo amporoj emr ‑|oz |rmkodzt„ mr emr dmn|cgy zm
ox|cgj igzm zcr`oz croct'@morgnogz Igzorogzimg — Ncy rotuaz ig hi`hor mr ampor NCRRt! jo|ogjig` mg zho hmp
zho igzorogzimg ceeodzt zho dmn|cgy’t dmn|oziziogottZcx tzrudzuro — Hi`hor zcxot igjudo dmn|cgiot zm rcito zho NCRR cgj ido ortcAinizoj dc|izca — Ainizoj cciacbiaizy me dc|izca rotuazt ig igdroctoj NCRRt ct dmn|cgiot
czzon|z zm jo|amy zho dc|izca nmtz oeeodzioayNcrfoz rczot — hi`hor igzorotz rczot igdrocto zho dmtz me dc|izca! rosuirig` c hi`hor NCRR
3<'2 (c) Osuizy(b) Osuizy(d) Jobz(j) Jobz(o) Osuizy
3<'4 Boemro.zcx NCRR > <'32-(3 — <':<)> <'2< (2</)
3<': (c) Oeeodzio zcx rczo > <'<0 & (<'94)(<'22) > <'20?
Ermn Osuczimg V3<'3^
Boemro.zcx NCRR > <'3?-(3 — <'20?)> <'2<0 (2<'0/)
(b) Bij cnmugz > 0'2 niaaimg-(3 — <'2<0)> *9'<8 niaaimg
3<'? <'29 > cezor.zcx rozurg-(3 — <'42)
Cezor.zcx rozurg > 39'0/
3<'5 RMR nocturo; Toaodz |rmkodzt C cgj O zm zmzca *34 niaaimg' M||mrzugizy dmtz it RMR >2<':/ emr |rmkodz D
\P nocturo; Toaodz |rmkodzt C cgj D zm zmzca *35 niaaimg' M||mrzugizy dmtz it RMR >25'</ emr |rmkodz O
7/23/2019 Chapter # 10 - Engineering Economy, 7 th editionLeland Blank and Anthony Tarquin
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3<'0 (c) NCRR > PCDD & rosuiroj rozurg > 8/ & :/> 32/
Zho 4/ ritf ecdzmr it dmgtijoroj cezor zho |rmkodz it ocauczoj6 gmz cjjoj zm zho NCRR
(b) Ocauczo zho |rmkodz cgj jozornigo zho RMR' Ie iz it 3?/ cgj Zmn rokodzt zho |rm|mtca!hit NCRR it oeeodzioay 3?/ |or yocr'
3<'8 Zho jobz |mrzimg me *38 niaaimg ro|rotogzt :?/ me zho zmzca'
Zmzca cnmugz me eigcgdig` > 38!<<<!<<<-<':?> *:<!<<<!<<<
3<'9 J.O nix; Jobz > 32 & 2< > *42 niaaimgOsuizy > ? & 3< > *3? niaaimg
/ jobz > 42-(42 & 3?) > 58// osuizy > 3?-:0 > 42/
J.O nix it 58.42
3<'3< (c) Butigott; caa jobz6 J.O > 3<< zm <
Og`igoorig`; caa jobz6 J.O > 3<< zm <
(b) Butigott; EP > 4<!<<<(E-\!:/!3)> 4<!<<<(3'<:)> *43!2<<
Dhodf it emr *43!2<< zm tzujogz amcg meeido
Og`igoorig`; EP > 2?!<<<(3) & 2?!<<<(E-\!0/!3)> 2?!<<<(3 & 3'<0)> *?3!0?<
Zpm dhodft; *2?!<<< zm |crogzt cgj *25!0?< zm drojiz ugimg
(d) Butigott; :/
Og`igoorig`; <'?(</) & <'?(0/) > 4'?/
3<'33 Eirtz Og`igoorig`; Ercdzimg jobz > 80-30? ≈ ?</
Ercdzimg osuizy > (30?.80)-30? ≈ ?</
Bctidcaay! c ?<.?< J.O nix
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Nijpotz Jooam|nogz; Ercdzimg jobz > (30?.52)-30? > 5:'5/
Ercdzimg osuizy > 52-30? > 4?':/
C||rmxinczoay! c 5?.4? J.O nix
3<'32 Dmn|cgy’t osuizy > ?<(<':<) > *2< niaaimg
Rozurg mg osuizy > ?-2< > <'2? (2?/)
3<'34 Zmzca eigcgdig` > 4 & : & 5 > *34 niaaimg
PCDD > (4-34)(<'3?) & (:-34)(<'<9) & (5-34)(<'<0)> 9':5/
3<'3: (c) PCDD3 > <'?(9/) & <'?(5/) > 0'?/
PCDD2 > <'2(9/) & <'8(8/) > 8'2/
\acg 3 hct c ampor PCDD
(b) Aoz x > dmtz me jobz dc|izca
PCDD3 > 8'2/ > <'?(9/) & <'?xx > 0':/
PCDD2 > 8'2/ > <'2(9/) & <'8xx > 8'</
\acg 3 dmtz me jobz `mot u| ermn 5/ zm 0':/6 \acg 2 ncigzcigt zho tcno dmtz'
3<'3? PCDD > dmtz me jobz dc|izca & dmtz me osuizy dc|izca> (<':)V<'550(8/) & <'444(3</)^ & (<'5)V(<':)(?/) & (<'5)(9/)^> <':V8'550/^ & <'5 V0':/^> 0'9<0/
3<'35 Tmao emr zho dmtz me jobz dc|izca! x
PCDD > 33'3/ > <'0?(0/) & (3. <'0?)(x)x > (33'3 — ?'2?)-<'2?
> 24':/
3<'30 (c) Jozornigo zho cezor.zcx dmtz me jobz dc|izca! Osuczimg V3<':^! cgj PCDD
Cezor.zcx dmtz me jobz dc|izca > 3<(3 . <'45) > 5':/Cezor.zcx PCDD > <'4?(5':/) & <'5?(3:'?/) > 33'55?/
7/23/2019 Chapter # 10 - Engineering Economy, 7 th editionLeland Blank and Anthony Tarquin
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Igzorotz dhcr`oj zm rooguo emr zho |rmkodz;
3:'< niaaimg(<'3355?) > *3!544!3<<
(b) Cezor.zcx PCDD > <'2?(3:'?/) & <'0?(5':/)
> 8':2?/
Igzorotz dhcr`oj zm rooguo emr zho |rmkodz;
3:'< niaaimg(<'<8:2?) > *3!309!?<<
Ct nmro cgj nmro dc|izca it bmrrmpoj! zho dmn|cgy ritft hi`hor amcg rczot cgjmpgt aott cgj aott me iztoae' Jobz dc|izca (amcgt) bodmnot nmro ox|ogtio cgjhcrjor zm cdsuiro'
3<'38 Zho ampotz PCDD cauo me 5'0/ mddurt cz zho jobz ercdzimg me <'4 mr *4<!<<< ig amcgt'
Zhit zrcgtaczot igzm eugjig` *0<!<<< ermn zhoir mpg eugjt'
3<'39 (c) Dmn|uzo cgj |amz PCDD emr ocdh J.O nix' Too |amz ig |rmbaon 3<'2< boamp'
J.O nix PCDD3<<.< 3:'?</0<.4< 33'::
5?.4? 3<'?4?<.?< 9'0<4?.5? 9'8:2<.8< 32':8
< . 3<< 32'?<
(b) J.O nix me ?</.?</ hct zho ampotz PCDD cauo'
7/23/2019 Chapter # 10 - Engineering Economy, 7 th editionLeland Blank and Anthony Tarquin
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3<'2< (c) Zho t|rocjthooz thmpt c ?</ . ?</ nix zm hco zho ampotz PCDD cz 9'0</'
(b) Nuazi|ay zho jobz rczo (dmaung D) by 3'3 zm cjj zho 3</ (dmaung J) cgj mbtoro zhogop |amz' Gmp jobz me 4?/ (J.O me 4?.5?) hct zho ampotz PCDD > 3<'38/'
3<'23 (c) < > 2!8<<!<<< — 395!<<<(\-C!i+!3<) — 2!8<<!<<<(\-E!i+!3<)
i+ > 0'</ (RCZO eugdzimg mg t|rocjthooz)
Boemro.zcx dmtz me jobz dc|izca it 0'</ |or yocr
(b) Zcx tcig`t > 395!<<<(<'44) > *5:!58<
GDE > 395!<<< . 5:!58< > *343!42<
< > 2!8<<!<<< — (343!42<)(\-C!i+!3<) — 2!8<<!<<<
i+ > :'0/ (RCZO eugdzimg)
Cezor.zcx dmtz me jobz dc|izca it :'0/ |or yocr
7/23/2019 Chapter # 10 - Engineering Economy, 7 th editionLeland Blank and Anthony Tarquin
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3<'22 (c) < > 39!<<<!<<< — 3!2<<!<<<(\-C!i+!3?) — 2<!<<<!<<<(\-E!i+!3?)
i+ > 5'?4/ (t|rocjthooz)
Boemro.zcx dmtz me jobz dc|izca it 5'?4/ |or yocr
(b) Zcx tcig`t > 3!2<<!<<<(<'29) > *4:8!<<<
GDE > 3!2<<!<<< . 4:8!<<< > *8?2!<<<
< > 39!<<<!<<< — (8?2!<<<)(\-C!i+!3?) — 2<!<<<!<<<
i+ > :'04/ (t|rocjthooz)
Cezor.zcx dmtz me jobz dc|izca it :'04/ |or yocr
3<'24Bmgj igzorotz > <'<5(4!3<<!<<<) > *94!<<< oory 5 nmgzht2Jiijogj toni.cgguca goz dcth eamp > *94!<<<(3 . <'42) > *54!2:<
Zho rczo me rozurg osuczimg |or 5.nmgzht mor 3?(2) toni.cgguca |orimjt it;
< > 4!3<<!<<< — 54!2:<(\-C!i+!4<) — 4!3<<!<<<(\-E!i+!4<)
i+ > 2'<:/ |or 5 nmgzht (t|rocjthooz)
(c) Gmnigca i+-yocr > 2(2'<:) > :'<8/ |or yocr
(b) Oeeodzio i+-yocr > (3'<2<:)2 — 3 > <'<:32 (:'32/ |or yocr)
3<'2: (c) Bcgf amcgCgguca amcg |cynogz > 8<<!<<<(C-\!8/!8)
> 8<<!<<<(<'30:<3)> *349!2<8
\rigdi|ca |cynogz > 8<<!<<<-8 > *3<<!<<<Cgguca igzorotz > 349!2<8 — 3<<!<<< > *49!2<8Zcx tcig` > 49!2<8(<':<) > *3?!584Oeeodzio igzorotz |cynogz > 49!2<8 — 3?!584 > *24!?2?Oeeodzio cgguca |cynogz > 24!?2? & 3<<!<<< > *324!?2?
Zho CP.bctoj i+ roaczimg it;
< > 8<<!<<<(C-\!i+!8) —324!?2?
7/23/2019 Chapter # 10 - Engineering Economy, 7 th editionLeland Blank and Anthony Tarquin
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(C-\!i+!8) > 324!?2? > <'3?::38<<!<<<
i+ > :'9?/ (RCZO eugdzimg)
Bmgj ittuoCgguca bmgj jiijogj > 8<<!<<<(<'<5) > *:8!<<<Zcx tcig` > :8!<<<(<':<) > *39!2<<Oeeodzio bmgj jiijogj > :8!<<< — 39!2<< > *28!8<<
Zho CP.bctoj i+ roaczimg it;
< > 8<<!<<<(C-\!i+!3<) . 28!8<< . 8<<!<<<(C-E!i+!3<)
i+ > 4'5</ (RCZO mr IRR eugdzimg)
Bmgj eigcgdig` it dhoc|or'
(b) Boemro zcxot; Bmgjt dmtz 5/ |or yocr! phidh it aott zhcg zho 8/ amcg' Zho cgtporboemro zcxot it zho tcno ct zhcz cezor zcxot'
3<'2? (c) Cgguca amcg |cynogz it zho dmtz me zho *35<!<<< jobz dc|izca' Eirtz! jozornigo zhocezor.zcx dmtz me jobz dc|izca'
Jobz dmtz me dc|izca; boemro.zcx (3.Zo) > 9/(3. <'22) > 0'<2/Cgguca igzorotz 35<!<<<(<'<0<2) > *33!242Cgguca |rigdi|ca ro.|cynogz > 35<!<<<-3? > *3<!550Zmzca cgguca |cynogz > *23!899
(b) Osuizy dmtz me dc|izca; 5'?/ |or yocr mg *:<!<<< it *25<< cggucaay'
Toz u| zho t|rocjthooz pizh zho zhroo toriot' Osuizy rczo it 5'?/! amcg igzorotz rczo it0'<2/! cgj |rigdi|ca ro.|cynogz rczo it 5'?/ tigdo zho cgguca cnmugz piaa gmz ocrgigzorotz cz zho osuizy rczo me 5'?/' Zho jieeorogdo ig \P cauot it;
Jieeorogdo > 2<<!<<< . \P osuizy amtz — \P me amcg igzorotz |cij— \P me amcg |rigdi|ca ro.|cynogz gmz tcoj ct osuizy
> *.25! 935
Zhit nocgt zho \P me zho toaaig` |rido ig zho euzuro nutz bo cz aoctz *25!935 nmrozhcg zho durrogz |urdhcto |rido zm ncfo c |mtizio rozurg mg zho igotznogz!cttunig` caa zho durrogz gunbort roncig tzcbao'
(d) Cezor.zcx PCDD > <'2(5'?/) & <'8(9/)(3.<'22)> 5'935/
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3<'25 Dmtz me osuizy dc|izca > 3<-(3 . <'<?)(34<)
> 8'3/
3<'20 By Osuczimg V3<'0^
Ro > <'92-24 & <'<42> <'<02 (0'2/)
3<'28 Zho zpm zcx rczot cro zho tcno emr osuizy eigcgdig` bodcuto tzmdf jiijogjt |cij zmtzmdfhmajort cgj mpgort cro gmz zcx jojudzibao aifo igzorotz it emr dmr|mrczo jobz'
3<'29 Ro > <'<42 & 3':3(<'<48)
> <'<8?5 (8'?5/)
3<'4< Jiijogj nozhmj; Ro > <'0?-33'?< & <'<4> <'<9?2 (9'?2/)
DC\N; Ro > <'<?? & 3'4(<'<4)> <'<9: (9':/)
3<'43 Jiijogj nozhmj; Ro > JU3 -\ & `> <'94-38'8< & <'<3?> <'<5:: (5'::/)
DC\N; (Zho rozurg cauot cro ig |ordogzt)Ro > Re & β(R n . Re )
> :'? & 3'39(:'9? — :'?)> ?'<:/
DC\N otzinczo me dmtz me osuizy dc|izca it 3':/ ampor'
7/23/2019 Chapter # 10 - Engineering Economy, 7 th editionLeland Blank and Anthony Tarquin
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3<'42 Actz yocr DC\N dmn|uzczimg; Ro > :'< & 3'3<(?'3 — :'<)> :'< & 3'23 > ?'23/
Zhit yocr DC\N dmn|uzczimg; Ro > 4'9 & 3'38(?'3 — 4'9)> 4'9 & 3':2 > ?'42/
Osuizy dmtzt tai`hzay nmro ig |crz bodcuto zho dmn|cgy’t tzmdf bodcno nmro macziaobctoj mg cg igdrocto ig bozc' Catm! zho tceo rozurg rczo jodroctoj <'3/ ig zho tpizdh ermn_T zm Ourm bmgjt'
3<'44 (c) Zmzca osuizy cgj jobz eugj it *3? niaaimg'
Osuizy PCDD > rozcigoj ocrgig`t ercdzimg (dmtz) & tzmdf ercdzimg (dmtz)> :-3?(0':/) & 5-3?(:'8/)> 4'894/
Jobz PCDD > ?-3?(9'8/) > 4'250/
PCDD > 4'894 & 4'250 > 0'35/
NCRR > PCDD & :/> 0'35 & :'<> 33'35/
(b) Jobz dc|izca `ozt c zcx brocf6 osuizy jmot gmz'
Cezor.zcx dmtz me jobz > 9'8/(3. <'42) > 5'55:/
Cezor.zcx PCDD > osuizy dmtz & jobz dmtz> :-3?(0':/) & 5-3?(:'8/) & ?-3?(5'55:/)> 5'33/
Cezor.zcx NCRR > 5'33 & :'< > 3<'33/
3<'4: C acr`o J.O nix mor zino it gmz hocazhy eigcgdicaay bodcuto zhit igjidczot zhcz zho|ortmg mpgt zmm tncaa me c |ordogzc`o me hit mr hor mpg cttozt (osuizy mpgorthi|) cgj itritfy emr drojizmrt cgj aogjort' Phog zho odmgmny it ig c ‘zi`hz nmgoy tizuczimg’cjjizimgca dcth cgj jobz dc|izca (amcgt! drojiz dcrjt! ozd') piaa bo hcrj zm mbzcig cgj oryox|ogtio ig zornt me zho igzorotz rczo dhcr`oj'
3<'4? Ie zho J.O nix me zho |urdhctor it zmm hi`h cezor zho buymuz cgj acr`o igzorotz|cynogzt (jobz torido) cro rosuiroj! zho gop dmn|cgy’t drojiz rczig` ncy bo jo`rcjoj'Ig zho oogz zhcz cjjizimgca bmrrmpoj eugjt cro goojoj! iz ncy gmz bo |mttibao zm mbzcigzhon' Cciacbao osuizy eugjt ncy hco zm bo jo|aozoj zm tzcy ceamcz mr `rmp ctdmn|ozizimg dhcaaog`ot zho dmnbigoj dmn|cgiot' Tudh oogzt ncy ti`gieidcgzay pocfogzho odmgmnid tzcgjig` me zho dmn|cgy'
7/23/2019 Chapter # 10 - Engineering Economy, 7 th editionLeland Blank and Anthony Tarquin
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3<'45 (c) Eirtz eigj dmtz me osuizy dc|izca utig` DC\N! phidh it zho NCRR
Ro > 4'< & <'9?(?'<) > 0'0?/
Eigj i+ mg osuizy igotznogz me *2?<!<<< cgj GDE me *:8!<<<
< > .2?<!<<< & :8!<<<(\-C! i+!0)
i+ > 8'</ 7 0'0?/
Zho ogzuro it cddo|zcbao
(b) Emr ?</ osuizy eigcgdig` cz 0'0?/ cgj ?</ jobz eigcgdig` cz 8/
PCDD > NCRR > <'?<(0'0?/) & <'?<(8/)> 0'80?/
Zho ogzuro it cddo|zcbao bodcuto 8'</ 7 0'80?/
3<'40 3<</ osuizy eigcgdig`
NCRR > 0'?/ it fgmpg' Jozornigo \P cz zho NCRR
\P > .2?<!<<< & 4<!<<<(\-C!0'?/!3?)> .2?<!<<< & 4<!<<<(8'82032)> .2?<!<<< & 25:!83:> *3:!83:
Tigdo \P 7 <! 3<</ osuizy eigcgdig` noozt zho NCRR rosuironogz
5</.:</ J.O eigcgdig`
Amcg |rigdi|ca > 2?<!<<<(<'5<) > *3?<!<<<Amcg |cynogz > 3?<!<<<(C-\!0/!3?)
> 3?<!<<<(<'3<909)> *35!:59 |or yocr
Dmtz me 5</ jobz dc|izca it 0/ emr zho amcg'
PCDD > <':(0'?/) & <'5(0/) > 0'2/NCRR > 0'2/
Cgguca GDE > |rmkodz GDE . amcg |cynogz> *4<!<<< — 35!:59 > *34!?43
Cnmugz me osuizy igotzoj > 2?<!<<< . 3?<!<<< > *3<<!<<<
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Dcaduaczo \P cz zho NCRR mg zho bctit me zho dmnnizzoj osuizy dc|izca'
\P > .3<<!<<< & 34!?43(\-C!0'2/!3?)> .3<<!<<< & 34!?43(8'99490)> *23!590
Tigdo \P 7 <6 c 5<.:< J.O nix catm noozt zho NCRR rosuironogz'Dmgdautimg; Bmzh eigcgdig` |acgt ncfo zho |rmkodz odmgmnidcaay czzrcdzio'
3<'48 (c) Eigj dmtz me osuizy dc|izca utig` DC\N'
Ro > :/ & 3'22(?/) > 3<'3/
NCRR > 3<'3/
Eigj i+ mg ?</ osuizy igotznogz'
< > .?!<<<!<<< & 3!4?<!<<<(\-C!i+!?)
i+ > 3<'9/ (RCZO mg t|rocjthooz)
Zho igotznogz it ncr`igcaay cddo|zcbao tigdo i+ 7 NCRR me 3<'3/
(b) Jozornigo PCDD cgj toz NCRR > PCDD' Emr ?</ jobz eigcgdig` cz 8/!
PCDD > NCRR > <'?(8/) & <'?(3<'3/) > 9'<?/
Zho igotznogz it cddo|zcbao! tigdo 3<'9/ 7 NCRR me 9'<?/
3<'49 (c) Dcaduaczo zho zpm PCDD cauot emr eigcgdig` cazorgczio 3 cgj 2
PCDD3 > <':(9/) & <'5(3</) > 9'5/
PCDD2 > <'2?(9/) & <'0?(3<'?/) > 3<'32?/
_to c||rmcdh 3! pizh c J.O nix me :</.5</
(b) Aoz x3 cgj x2 bo zho ncxinun dmtzt me jobz dc|izca emr ocdh |acg! rot|odzioay
Cazorgczio 3; 3</ > PCDD3 > <':(9/) & <'5(x3)
x3 > 3<'50/
Jobz dc|izca dmtz dmuaj igdrocto ermn 3</ zm 3<'50/
Cazorgczio 2; 3</ > PCDD2 > <'2?(9/) & <'0?(x2)
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x2 > 3<'44/
Jobz dc|izca dmtz pmuaj hco zm jodrocto ermn 3<'?/ zm 3<'44/
3<':< Zpm igjo|ogjogz! rooguo |rmkodzt pizh jieeorogz aiot' Ectzotz tmauzimg it zm eigj CP cz
NCRR emr ocdh |rmkodz' Toaodz caa zhmto pizh CP 7 <' Eigj PCDD eirtz'
Osuizy dc|izca it :</ cz c dmtz me 0'?/ |or yocr
Jobz dc|izca it ?/ |or yocr! dmn|mugjoj sucrzoray' Oeeodzio rczo cezor zcxot it
Cezor.zcx jobz i+ > V(3 & <'<?-:): . 3^ (3. <'4) (3<</)> ?'<9?(<'0) > 4'?55/ |or yocr
PCDD > <':(0'?/) & <'5(4'?55/) > ?'3:/ |or yocr
NCRR > PCDD > ?'3:/
(c) Cz NCRR > ?'3:/! toaodz bmzh igjo|ogjogz |rmkodzt (rmp 30)
(b) Cz i+ > 3:'<:/! |rmkodz P it cddo|zcbao tigdo iz rozurgt tubtzcgzicaay nmro zhcg 2/cbmo NCRR > ?'3:/' Hmpoor! |rmkodz R hct c rozurg me 5':</' Ie zho 2/ ritf cttottnogz it rocaitzid cgj in|mtoj! |rmkodz R it gmz cddo|zcbao bctoj mg zmm nudhritf'
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3<':3 (c) Tzcg; Tzmdf cauo igdrocto; <'3<(2<!<<<) > *2<<<Osuizy cauo cz yocr.ogj; *22!<<< mr c 3</ igdrocto
Zhorotc; Dmgjm cauo igdrocto; <'3<(3<<!<<<) > *3<!<<<Osuizy cauo cz yocr.ogj; *4<!<<< mr c ?</ igdrocto
(b) Tzcg; Tzmdf cauo jodrocto; .<'3<(2<!<<<) > *.2<<<Osuizy cauo cz yocr.ogj; *38!<<< mr c 3</ igdrocto
Zhorotc; Dmgjm cauo jodrocto; .<'3<(3<<!<<<) > *.3<!<<<Osuizy cauo cz yocr.ogj; *3<!<<< mr c ?</ jodrocto
(d) _gjor hi`h aoorc`o tizuczimgt! zho `cig mr amtt it nuazi|aioj by zho aoorc`o ecdzmr' Ie zho igotznogz `mot jmpg c tncaa cnmugz! zho hi`h aoorc`o amtot nudh nmro zhcgzho ugaoorc`oj igotznogz (*2<<< amtt emr Tzcg t' c *3<!<<< amtt emr Zorotc)' Pizh`cigt! zho rozurg mg osuizy dc|izca it nudh acr`or emr zho hi`hay aoorc`o igotznogz!
buz iz ncy bo nudh nmro ritfy'
3<':2 Pi > 3-8 > <'32?
3<':4 Τti > 5< & :< & 8< & 4< & 2< > 24<
P3 > 5<-24< > <'25P2 > :<-24< > <'30P4 > 8<-24< > <'4?P: > 4<-24< > <'34P? > 2<-24< > <'<9 (Tun it 3'<<)
3<':: T > 3 & 2 & 4 &‥ & 3< > 3<(33)-2 > ??
(c) PD > 4-?? > <'<??
(b) PK > 3<-?? > <'382
3<':? Rczig`t by czzribuzo pizh 3<< emr nmtz in|mrzcgz'Am`id; E > 3<<
_ > ¾ E > ?<T > <'0 _ > <'0(?<) > 4?R > 2T > 2(4?) > 0<
Czzribuzo In|mrzcgdo TdmroE 3<<T 4?_ ?<R 0<
2??
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Poi`hzig`! Pi > Tdmro-2??
Czzribuzo Pi E <'49T <'3:
_ <'2<R <'203'<<
3<':5 Rczig`t by czzribuzo pizh 3<< emr nmtz in|mrzcgz'
Am`id; $3 > <'9<($?) > <'9<(3<<) > 9<$2 > <'3<(3<<) > 3<$4 > <'4<(3<<) > 4<$: > 2($4) > 2(4<) > 5<$? > 3<<
$5 > <'8<($:) > <'8<(5<) > :8
Czzribuzo In|mrzcgdo3 92 34 4: 5? 3<5 :'8
44'8
Poi`hzig`! Pi
> Tdmro-44'8
Czzribuzo Pi]]]]]] 3 9-44'8 > <'202 3-44'8 > <'<44 4-44'8 > <'<9: 5-44'8 > <'38? 3<-44'8 > <'4<5 :'8-44'8 > <'3:
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3<':0 Dcaduaczo Pi > in|mrzcgdo tdmro-tun cgj tmao emr R k
Uido |rotijogz
Czzribuzo! In|mrzcgdo Uik cauot]]]]
i tdmro Pi 3 2 4]]3 2< <'3< ? 0 3<2 8< <':< :< 2: 324 3<< <'?< ?< 2< 2?
Tun > 2<< 9? ?3 :0 > R k cauot
Toaodz cazorgczio 3 tigdo R3 it acr`otz'
Cttitzcgz ido |rotijogz
Czzribuzo! In|mrzcgdo Uik cauot]]]]
i tdmro Pi 3 2 43 3<< <'?< 2? 4? ?<2 8< <':< :< 2: 324 2< <'3< 3< : ?
Tun > 2<< 0? 54 50 > R k cauot
Pizh R3 > 0?! toaodz cazorgczio 3
Rotuazt cro zho tcno! oog zhmu`h zho U\ cgj Cttz' U\ rczoj m||mtizo mg ecdzmrt 3 cgj 4'Hi`h tdmro mg czzribuzo 3 by Cttz' U\ it bcacgdoj by zho U\’t tdmro mg czzribuzot 2 cgj 4'
3<':8 (c) Toaodz C tigdo \PC
it acr`or'
(b) Dcaduaczo R k cgj uto ncgc`or tdmrot emr czzribuzot'
Pi > In|mrzcgdo tdmroTun
Czzribuzo! In|mrzcgdo R k]]]]]]] i by ncgc`or Pi C B]]3 8< <':8 <':8 <':42 4? <'23 <'<0 <'234 4< <'38 <'38 <'35: 2< <'32 <'<4 <'32
35? <'05 <'92
Zhoroemro! toaodz B
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(d) Dcaduaczo R k cgj uto zrcigor tdmrot emr czzribuzot'
Czzribuzo In|mrzcgdo R k]]]]]] i (by zrcigor) Pi C B]]3 8< <'25 <'25 <'24
2 8< <'25 <'<9 <'254 3<< <'42 <'42 <'29: ?< <'35 <'<: <'35
43< <'03 <'9:
Toaodz B
Dmgdautimg; 2 nozhmjt igjidczo B cgj 3! zho \P nozhmj! igjidczot C
3<':9 Cgtpor it (d)
3<'?< Cgtpor it (b)
3<'?3 Cgtpor it (c)
3<'?2 Cgtpor it (b)
3<'?4 Osuizy > :3-03 > ?0'0/Jobz > 4<-03 > :2'4/
Cgtpor it (j)
3<'?: PCDD > ?-3<(34'0) & 2-3<(8'9) & 4-3<(0'8)> 3<'90/
Cgtpor it (d)
3<'?? Boemro.zcx RMR > cezor.zcx RMR-(3. Zo)> 33'2/-(3.<'49)> 38':/
Cgtpor it (d)
3<'?5 Hitzmridca PCDD > <'?(33/) & <'?(9/) > 3</
Aoz x > dmtz me osuizy dc|izca
PCDD > osuizy ercdzimg(dmtz me osuizy) & ercdzimg me jobz(dmtz me jobz)
3</ > <'2?(x) & <'0?V9/(3'2)^
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x > (3< . 8'3)-<'2? > 0'5/
Cgtpor it (c)
3<'?0 Τti > ?? & :? & 8? & 4< & 5< > 20?
P3 > ??-20? > <'2<
Cgtpor it (b)
3<'?8 T > 3 & 2 & 4 &‥ & 8 > 8(9)-2 > 45
PD > 5-45 > <'355
Cgtpor it (c)
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Tmauzimg zm Dcto Tzujy! Dhc|zor 3<
Zhoro it gmz capcyt c joeigizio cgtpor zm dcto tzujy oxorditot' Horo cro oxcn|ao rot|mgtot
PHIDH IT BOZZOR . JOBZ ME OS_IZY EIGCGDIG@=
3' Toz NCRR > PCDD
PCDD > (/ osuizy)(dmtz me osuizy) & (/ jobz)(dmtz me jobz)
Osuizy; _to Os' V3<'0^
Ro > <'?< & <'<? > 8'44/3?
Jobz; Igzorotz it zcx jojudzibao6 uto Ost' V3<'?^ cgj V3<'5^'
Zcx tcig`t > igzorotz(zcx rczo)> Vamcg |cynogz — |rigdi|ca |mrzimg^(zcx rczo)
Amcg |cynogz > 0?<!<<<(C-\!8/!3<) > *333!004 |or yocrIgzorotz > 333!004 — 0?!<<< > *45!004
Zcx tcig`t > (45!004)(<'4?) > *32!80<
Dmtz me jobz dc|izca it i+ ermn c \P roaczimg;
< > amcg cnmugz — (cgguca |cynogz cezor zcxot)(\-C!i+!3<)> 0?<!<<< — (333!004 — 32!80<)(\-C!i+!3<)
(\-C!i+!3<) > 0?<!<<< - 98!9<4 > 0'?842
i+ > ?'40/ (RCZO eugdzimg)
\acg C (?<.?<); NCRR > PCDDC > <'?(?'40) & <'?(8'44) > 5'8?/
\acg B (<.3<</); NCRR > PCDDB > 8'44/
2' C; ?<—?< J—O eigcgdig`
_to roaczimgt ig dcto tzujy tzczonogz cgj zho rotuazt ermn Suotzimg $3'
ZI > 4<<!<<< — 45!004 > *254!220Zcxot > 254!220(<'4?) > *92!34<
Cezor.zcx GDE > 4<<!<<< — 0?!<<< — 45!004 — 92!34<> *95!<90
Eigj |acg iC+ ermn CP roaczimg emr *0?<!<<< me osuizy dc|izca
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< > (dmnnizzoj osuizy dc|izca)(C-\!iC+!g) & T(C-E! iC+!g) & cezor zcx GDE< > .0?<!<<<(C-\!iC+!3<) & 2<<!<<<(C-E!iC+!3<) & 95!<90
iC+ > 0'50/ (RCZO eugdzimg)
Tigdo 0'50/ 7 PCDDC > 5'8?/! |acg C it cddo|zcbao'
B; <—3<< J—O eigcgdig`
_to roaczimgt it zho dcto tzujy tzczonogz
Cezor zcx GDE > 4<<!<<<(3—<'4?) > *39?!<<<
Caa *3'? niaaimg it dmnnizzoj' Eigj iB+
< > .3!?<<!<<<(C-\!iB+!3<) & 2<<!<<<(C-E!iB+!3<) & 39?!<<<
iB+ > 5'53/ (RCZO eugdzimg)
Gmp 5'53/ 1 PCDDB > 8'44/! |acg B it rokodzoj'
Rodmnnogjczimg; Toaodz |acg C pizh ?<.?< eigcgdig`'
4' T|rocjthooz thmpt zho hcrj pcy (jooam|t jobz.roaczoj dcth eampt emr ocdh yocr) cgj zho octypcy (utot dmtzt me dc|izca ermn $3) zm |amz PCDD' Iz it thc|oj jieeorogzay zhcg zho PCDDduro ig Ei`uro 3<.2'