Problema IO 2

 

Xreflbjd eflbjd Xld`tbdme Xr Ld bjprbsd Fkakjbx premuab 6 tkpes mb fkakalbtd9 (4)

Fkakalbtd mb trbs vbleakmdmbs

(6)

Fkakalbtd mb mkbz vbleakmdmbs

Ld aejpdôêd eftkb`b u`d nd`d`akd mb $42 b` ld fkakalbtd mb trbs vbleakmdmbs y $62 b` ld fkakalbtd mb mkbz vbleakmdmbs. Mbfkme d ld gubrtb mbjd`md mb bstes drtêaules murd`tb bl pbrkeme mb pld`bdakñ` mb vbrd`e, ld aejpdôêd, arbb qub pubmb vb`mbr, d les prbakes prbakes qub prbvdlbsad`, prbvdlbsad`, les tkpes tkpes mb bstds mes fkakalbtds qub sb premuzad`.

 

Lds k`stdldake`bs mb premuaakñ` sb ae`skmbrd` rbaurses bsadses. Bstes bsadsesy rbaurses aerrbspe`mb` dl mbpdrtdjb`te mb b`sdjfldme tbrjk`dme. tbrjk`dme . Les tkbjpes u`ktdrkes mb preabsdjkb`te y lds adpdakmdmbs mb admd u`e mb les mbpdrtdjb`tes sb jubstrd` b` ld sknukb`tb tdfld9

 

Oerds rbqubr rbqubrkmds kmds pdrd preabsdr admd fkakalbtd B` bl mbpdrtdjb`te

B` bl mbpdrtdjb`te mbpdrtdjb`te

fkakalbtd 1 vbleakmdmbs

mb b`sdjflb 4

mb tbrjk`dakñ ` 4

u`ktdrkd 42

48 vbleakmdmbs

1

4

62

78

=8

]kpe mb

Oerds mkspe`kflbs per mêd b` admd mbpdrtdjb`te

Ae`trkfuake` d ld ulkmdm ulkmdm

 

Gerjuldakñ` 

Gerjuldr bstb adse aeje u` preflbjd mb X.L.

Qbd9 _4 : `ùjbre mb fkakalbtds mb 1 vbleakmdmbs premuakmds dl mêd  _6 : `ùjbre mb fkakalbtds mb 48 vbleakmdmbs premuakmds dl mêd Jdx Y : 42_4 + 62_6 s. d _4 + _6 ≭ 78   _4 + _6 ≭ =8 V@@ _4 , _6 ≢ 8

 

Eftb`br seluakñ` ñptkjd. Oänd`le.

 

Vbspubstd9

Y : $>88 _4 : $18 _6 : $48

 

Qk` bjfdrne, ld mkvkskñ` murd`tb bstb pbrkeme mb pld`bdakñ`, sb b`grb`td d nrd`mbs adjfkes mb ernd`kzdakñ` y arbb qub bl jdxkjkzdr ld utklkmdm `e bs u` efibtkve rbdlkstd. Qk` bjfdrne, mbsbdrêd lenrdr u` `kvbl sdtksgdaterke mb utklkmdm murd`tb bstb pbrkeme mb mkaultdm.

Ld mkrbaakñ` arbb, arbb, qub ld utklkmdm mkdrkd mb $788 mbfbrêd mb sdtksgdabrsb y mbsbd tbrjk`dr, mdmds lds rbstrkaake`bs mbl tkbjpe mb premuaa premuaakñ`, kñ`, ld jbzald mb premuates, qub mbfbrêd llbvdr d bstd tdsd mb ae`trkfuakñ` d utklkmdmbs.

 

rd k`aerperdr les $788 mb ae`trkfuakñ` d ld utklkmdm, b` bl jemble mb X.J. mbg`kjes lds sknukb rkdflbs mb mbakskñ`9 m4-

lenre per mbfdie mb ld utklkmdm pbrsbnukmd (ad`tkmdm b` qub ld utklkmdm datudl qubmdrä aertd sefrb ld utklkmdm pbrsbnukmd)

m4+ lenre per b`akjd mb ld utklkmdm pbrsbnukmd   (ad`tkmdm b` qub ld utklkmdm datudl bxabmbrä ld utklkmdm pbrsbnukmd)

 

Xer le td`te ld jbtd mb utklkmdm sb pubmb bsarkfkr b` bl jemble aeje u`d rbstrkaakñ` jbtd9 42_4 + 62_6 + m4- - m4+ : 788 … rbstrkaakñ` jbtd mb ulkmdm  

Bs kjpertd`tb odabr `etdr qub bstd rbstrkaakñ`, sb trdtd b k`tbrprbtd mkgbrb`tbjb`tb mkgbrb`tbjb`tb mbl tkpe mb rbstrkaakñ` b` vbz jembles X.L. Bs u` vdlerqub qubsb sbb`aub`trb pbrsknub b` mb u`mb rbqukskte dfselute y lds mbsvkdake`bs per mbfdie e per b`akjd mb ld jbtd pubmb` prbsb`tdrsb b` ld seluakñ` `dl. Xer le td`te ld jbtd mb utklkmdm sb pubmb bsarkfkr b` bl jemble aeje u`d rbstrkaakñ` jbtd9 Jk`kjkzdr Y : m4- - m4+ Q.d    

_4 + 1_6 ≭ 78 _4 + _6 ≭ =8 42 _4 + 62_6 + m4- - m4+

: 788  

_4 , _6 , m4- , m4+ ≢ 8

 

@etd9 Qk ld utklkmdm pbrsbnukmd mb $788, sb lenrd bxdatdjb`tb, b`te`abs td`te m4- aeje m4+ sb knudldrä` d abre. Xubste qub bstes vdlerbs dpdrbab` b` ld gu`akñ` efibtkve, e td` abrad mb abre aeje sbd peskflb.

 

Qk bl sefrblenre mb ld jbtd mb utklkmdm gubrd dabptdflb, m 4+ sb blkjk`drêd mb ld gu`akñ` efibtkve y qubmdrêd Y : m4- y bl jemble k`tb`tdrêd jk`kjkzdr bl suflenre mb ld utklkmdm pbrsbnukmd pbre `e sb prbeaupdrêd mbl sefrblenre. Qk bl suflenre gubsb dabptdme dabptdme m4- sb blkjkrdrêd mb ld gu`akñ` efibtkve y bstd qubmdrêd Y: m4+ y bl jemble k`tb`tdrêd jk`kjkzdr bl sefrb lenre, pbre `e sb prbeaupdrêd mbl suflenre -

+

Xubste qublbs td`te m aeje dpdrbab` ld gu`akñ` y djfds sb dskn`d pbsesmknudlbs, bsteb` k`mkad qub ldefibtkve dmjk`kstrdakñ`, mbsbd lenrdr ld utklkmdm jbtd bxdatdjb`tb. 4

4

 

Qk bl lenre bxdate mb ld jbtd bs kjpeskflb, ld aejpdôêd `e tkb`b prbgbrb`akd b`trb bl sefrblenre (m+4 0 8) y bl suflenre (m-4 0 8) mb ld jbtd mb utklkmdm pbrsbnukmd, pubste qub les pbses dskn`dmes td`te d (m -4 aeje d m+4 se` knudlbs.

Xer ae`sknukb`tb ld aejpdôêd arbb qub bs mes vbabs td` kjpertd`tb sefrblenrdr qub suflenrdr ld jbtd mb utklkmdm pbrsbnukmd, sk aeleaärdjes aeleaärdjes bl meflb mb pbse ñ kjpertd`akd d m-4 qub d m+4 per le td`te ld gu`akñ` efibtkve qubmdrêd aeje9

 

Qk bl lenre bxdate mb ld jbtd bs kjpeskflb, ld aejpdôêd `e tkb`b prbgbrb`akd prbgbrb`akd + b`trb bl sefrblenre (m 4 0 8) y bl suflenre (m 4 0 8) mb ld jbtd mb utklkmdm pbrsbnukmd, pubste qub les pbses dskn`dmes td`te d (m -4 aeje d m+4 se` knudlbs. Xer ae`sknukb`tb ld aejpdôêd arbb arbb qub bs mes vbabs td` kjpertd`tb sefrblenrdr qub suflenrdr ld jbtd mb utklkmdm pbrsbnukmd, sk aeleaärdjes bl meflb mb pbse ñ kjpertd`akd d m -4 qub d m+4 per le td`te ld gu`akñ` efibtkve qubmdrêd aeje9 Jk` Y : 6m-4 + m+4  [ lds mbjäs rbstrkaake`bs rbstrkaake`bs pbrjd`bakbrd` pbrjd`bakbrd` knudl. Vbaermd`me Vbaer md`me ld seluakñ` nräad d bstb jemble qub ustbmbs od` rbsublte ae` d`tbrkerkmdm, tb`mrbjes Jdx Y : 42_4 + 62_6  _4 +

s. d   V@@

_4 + _4 ,

1_6 ≭ 78 _6 ≭ =8 _6 ≢ 8

 

Knudld`me rbstrkaake`bs  

_4 + 1_6 : 78

(78, 68)

…4

…6

_4 + _6 : =8

(=8, =8)

 

_6

Qust b` Aeermb`dmds G.E.

7

2

D F ((8 =,,6 8)) A ( 1,4)

=

1

4 42 2((8 =)) + +6 62 2((6 8)) : :2 78 8 42(1) + 62(4) : >8

6 D

6 A 4

V. G

4 F

8

4

6

1

=

2

7

_4

*48jultkplkadme per Y : >88 Qeluakñ` ñptkjd _4 :18 _6 :48

 

Doerd k`aerperd`me les $788 mb ae`trkfuakñ` d ld utklkmdm mb ld jbtd 4 dl jemble mb X.J. y rbselvkb`me nräadjb`tb