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NDSOXOCNC 9 CB LN RKOCNC 4

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Lns prbhbrbkdons cb uk d`ksugoc`r ndbrdn cb l`s iobkbs Q> y Q9 vobkbk cncns p`r ln somuobktb bxprbsoôk6 R(Q>, Q9) 7 Q>Q9  R  R   (( Q  > , Q 9 ) 7 Q  >∝ Q  9  9 Q   9 R   (( Q , _  ) 7 Q ∝_  7_  97_ Q  >  >7 Q R  Q  Q. 75,>,9,4,3,2,8,=,1,?,>5…45

_7 5,>,9,4,3,2,8,=,1,?,>5… 45 Durvns cb okcohbrbkdon n. °Dôg` bs ssu u gnpn cb cb durvns cb cb okcohbrbkdon okcohbrbkdon0 0 D`kso D`ksocbrb cbrb ln durvn durvn cb okcohbr okcohbrbkdon bkdon c cb b kovbl 45, °quï p` cb dbstns cb d`ksug` rbd`mb0 >555 ?55 155 =55 855 255 355 455 955 >55 5

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2

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>2

95 R

92

45

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i. °U`r quï bxprbsoôk vobkb cncn ln pbkcobktb cb dunlquobr durvn cb okcohbrbkdon0 °^uï oktbrprbtndoôk bd`kôgodn bkb0 Dnldölbln pnrn ln hukdoôk cb ulocnc cncn. Bvnlöb codan pbkcobktb pnrn lns d`giokndo`kbs cb iobkbs (8, 2) y (>5,4).

UBKCOBKSB7

 Γ y >5 ∙8 3 7 YGT 7 7 79  Γ x 2 ∙4 9

Ln YGT pnrn bstb d`kfukt` cb iobkbs bs 9, l` qub gnkobstn qub bl d`ksugoc`r bstn cospubst` n rbkukdonr n c`s ukocncbs cbl iobk x n dngio` cb ukn ukocnc ncodo`knl cbl iobk y.  d. °^uï `trns hukdo`kbs cb ulocnc rbprbsbktnk tngioïk lns prbhbrbkdons cb bstn d`ksugoc`r0 Dnldulb pnrn dncn ukn cb bllns ln YGT.

 

9.

Ln rbktn cb uk d`ksugoc`r bs cb 9.255 €/gbs. Bstn rbktn rb ktn ln mnstn çktbmrngbktb bk nlogbkt` (Q>) y vbsc` (Q9), duy`s prbdo`s s`k, rbspbdvngbktb, U> 72€ y U9 7>5€. n. Bxprbsb ln rbstroddoôk prbsupubstnron cb bstb d`ksugoc`r b okcoqub duîl bs su d`kfukt` prbsupubstnro`.

DN DN

4.

{

{

  ( Q , _  ) )  p x x + p y y ≣ Y

}

  ( Q , _  ) ) 2 x + >5 y ≣ 9255

}

Tbn uk d`ksugoc`r duyns prbhbrbkdons ndbrdn cbl iobk Q> y cbl Q9 vobkb cncns p`r ln somuobktb

hukdoôk cb ulocnc6 R (Q>, Q9)7 Q> 5.> Q9 5.? Ln rbktn cb bstb d`ksugoc`r pnrn uk pbrç`c` cb bgp` b gp` nsdobkcb n 9.555 u.g., sobkc` U>725 u.g. y U97 >55 u.g.  TB YB^ROBYB ANLLNY6

R  ( Q > , Q 9 )  Q >  Q 9 7

5,>

5,>

5,?

5,?

 Gnx Q  , Q  7 Q >  Q 9 >

9

s . n 2 5 Q >+ >55  Q 9 ≣ 9555

n) Lns hukdo hukdo`kbs `kbs cb cb cbgnkcn cbgnkcn d`kco d`kcodo`kn do`kncns cns p pnrn nrn ngi`s ngi`s iobkbs iobkbs

5,>

5,?

 L7 Q >  Q 9 + κ (∙25 Q >∙>55 Q 9 ∙9555)

}

∉L 75.> Q ∙> 5,? + κ 75 ∉ Q >  Cbgnkcns d`kcodo`kncns ∉L ∙5 , > 7 5. ? Q > + κ 75 ∉ Q 9 ∉L 7∙25 Q >∙>55 Q 9∙9555 75 ∉κ  

i) Tbkcn cb bxpnksoôk

 

∙5,?

}

 Ugm Q >  U x Q > 5.> Q >   25 Q > Tbkcn Tbk cn cb bxpnkso bxpnksoôk ôk ≪ 7 7 ∙ 5,>  Ugm Q 9  Ux Q 9 >55 Q 9 5.? Q 9

n) D`ksug D`ksug` ` ôpg ôpg` `c cbl bl d`k d`ksug sugoc` oc`rr