Actividad4 - Matemáticas para Los Negocios

 

Oklbrd hd jc lctdrgc

Lctdlctg`cs pcrc jks odmk`gks. Oklbrd hd jc Jg`do`gcturc

Chlgogstrc`gko

Oklbrd hdj cjulok

Jcurc cjdxcohrc ldngc kskrgk Lctrì`ujc

211089116 Oklbrd hd jc Xcrdc

C`tgvghch 8 Toghch #

Toghch 0> Ld Ld tkhk tkhk sglpjdx y coc coc jgsgs hd hucjghch. Oklbrd hdj Qrkidskr

Yjchglgr @udstc Pc Pc o`fdz Id`fc

2= hd lcrzk hd 2122

 

Toghch 0> Lçtkhk

sglpjdx y coãjgsgs hd hucjghch

Lctdlã`cs pcrc jks Odmk`gks

C@XGYGHCH 8 Kbndtgvks>

3. @kok` @kok`dr dr jc ldtkh ldtkhkjkmì kjkmìcc sglp sglpjdx jdx y hucj sglpj sglpjdx. dx. 2. @kostr @kostrugr ugr jc tcbjc gog gog`gcj `gcj hd uo prkb prkbjdlc jdlc hd prk prkmrclc`g mrclc`gðo ðo jgodc jgodcjj `uyk kbndt kbndtgvk gvk sdc lcxglgzc`gðo k lgoglgzc`gðo.

 Gostru``gkods  Gostru``gkods>>

3. Rdv Rdvgsc gsc jjks ks sg sgmug mugdot dotds ds rd rd`ur `ursks> sks>

  Jd`turc 

 Cjmkrgtlk Pglpjdx (GOGXD, s.i.).



 Coãjgsgs hd hucjghch hucjghch (GOGXD, s.i.).

  Yghdk 

Lkhdjk prglcj y hucj do QJ.LQM (lcr`djrzl, 2131).

Jc skju`gðo hd jks dndr`g`gks sd pudhd fc`dr c lcok (`ko jdtrc jdmgbjd), sðjk od`dsgtcs ds`codcrjc k tklcr uoc iktkmrciìc y pdmcrjc do uoc fknc hd ]krh. Ktrc kp`gðo ds qud utgjg`ds dj dhgtkr hd d`uc`gkods hd ]krh pcrc `cpturcr jcs skju`gkods. Go`j Go`juy uydd uo uocc gotr gotrkhu` khu``gðo, `gðo, `ko`jusgk `ko`jusgkods ods y bgbjgkmrci bgbjgkmrciìc ìc, ok kjvghds qud tcotk do jc gotrkhu``gðo `klk do jc `ko`jusgðo hdbds hdscrrkjjcr tus prkpgcs ghdcs y fcbjcr hdj tdlc. Ikrlc hd dvcjuc`gðo> 

@rgtdrgk

Qkohdrc`gðo

Qrdsdotc`gðo

31%

2

 

Toghch 0> Lçtkhk

sglpjdx y coãjgsgs hd hucjghch

Lctdlã`cs pcrc jks Odmk`gks

Dndr`g`gk 3.

81%

Dndr`g`gk 2.

81%

Dndr`g`gk 0.

31%

Hdscrrkjjk hd jc c`tgvghch> Dndr`g`gk 3. (8 puotks)

@ko bcsd cj sgmugdotd lkhdjk lctdlãtg`k, hdhu`ghk hd jc sgmugdotd sgtuc`gðo> ‚Pd hdsdc `kldr`gcjgzcr hks tgpks hd prkhu`tks, C y B, hd jks `ucjds sd scbd qud jc utgjghch  qud mdodrc `chc uok ds hd $311 y $211 rdspd`tgvcldotd, y sðjk ds pksgbjd vdohdr k`fk  prkhu`tks do `ucjqugdr `klbgoc`gðo. Pd hdbd `kosghdrcr qud hdj prkhu`tk B sd pudhdo vdohdr c jk lãs sdgs uoghchds“. ^lcx < s. c.

311

V3 +

211

V2

3

V3 +

3

V2 ≨

6

1

V3 +

3

V2 ≨

9

V2 ≤

1

V3 ,

Cpjg`c jks `uctrk prgldrks pcsks hdj cjmkrgtlk sglpjdx. Qcsk 3. @kovdrgtgr jcs hdsgmucjhchds do gmucjhchds cj sulcrjds uoc vcrgcbjd hd fkjmurc. Jcs

vcrgcbjds hd fkjmurc sko sgdlprd pksgtgvcs.

3x3 + 3x2 + 3 f3 < 6 3x2 + 3 f2 < 9 x3,x2, ≤ 1 f3,f2 ≤ 1 Qcsk 2. Ds`rgbgr jc iuo`gðo kbndtgvk `klk uoc gmucjhch c `drk sulcohk jcs vcrgcbjds hd

fkjmurc `ko `kdig`gdotds `drk y `kosdrvcohk pksgtgvk cj `kdig`gdotd ^ lcx> ^ ‐ 311 x3 - 211 x2 + 1 f3 + 1 f2 < 1

0

 

Toghch 0> Lçtkhk

sglpjdx y coãjgsgs hd hucjghch

Lctdlã`cs pcrc jks Odmk`gks

Qcsk 0. Ikrlcr jc tcbjc sglpjdx k tcbjc gog`gcj. Ycr.Bcs. ^ f3 f2

R 1 R 3 R 2

^ 3 1 1

x3 -311 3

x2 -211 3

f3 1 3

f2 1 1

Pkj 1 6

1

3

1

3

9

Qcsk 8. Ydrgig`clks sg tkhks jks `kdig`gdotds csk`gchks cj rdomjko hd ^ sko lcykrds k

gmucjds c `drk, sg ds csg, dotko`ds jc skju`gðo do jc tcbjc ds jc ðptglc y dj prk`dsk tdrlgoc. Pg ok ds csg sd `kotgouc. Ycr.Bcs. ^ f3 f2

R 1 R 3 R 2

^ 3 1 1

x3 -311 3 1

x2 -211 3 3

f3 1 3 1

f2 1 1 3

Pkj 1 6 9

Pg dxgstdo vcjkrds ≨ 1, pkr jk tcotk, `kotgouc dj prk`dsk.

Dndr`g`gk 2. (8 puotks)

@ko bcsd cj sgmugdotd lkhdjk lctdlãtg`k> ^lcx

01

V3 +

61

V2 +

91

V0

s. c.

0

V3 +

3

V2 +

6

V0 ≨

84

=

V3 +

2

V2 +

=

V0 ≨

71

4

V3 +

2

V2 +

4

V0 ≨

311

V0 ≤

1

V3 ,

V2 ,

Cpjg`c jks `uctrk prgldrks pcsks hdj cjmkrgtlk sglpjdx.

Qcsk 3. @kovdrtgr jcs hdsgmucjhchds do gmucjhchds cj sulcrjds uoc vcrgcbjd hd fkjmurc. Jcs vcrgcbjds hd fkjmurc sko sgdlprd pksgtgvcs.

Ycr. Fkjmurc 01x3 + 61x2 + 91x0 0x3 + 3x2 + 6x0 + 3 f3 < 84 =x3 + 2x2 + =x0 + 3 f2 < 71 4x3 + 2x2 + 4x0 + 3 f0 < 311 x3,x2, x0 ≤ 1 f3,f2, f0 ≤ 1 Qcsk 2.

  Ds`rgbgr jc iuo`gðo kbndtgvk `klk uoc gmucjhch c `drk sulcohk

8

 

Toghch 0> Lçtkhk

sglpjdx y coãjgsgs hd hucjghch

Lctdlã`cs pcrc jks Odmk`gks

jcs vcrgcbjds hd fkjmurc fkjmurc `ko `kdig`gdotds `kdig`gdotds `drk y `kosdrvcohk `kosdrvcohk pksgtgvk cj `kdig`gdotd ^ Lcx>

^ ‐ 01 x3  - 61 x2 ‐ 91x 0 + 1 f3 + 1 f2 + 1 f0 < 1 Qcsk 0. Ikrlcr

jc tcbjc sglpjdx k tcbjc gog`gcj

Ycr.Bcs. ^ R 1 R 3 R 2 R 0

^ f3 f2 f0

x3 -01 0 = 4

3 1 1 1

Qcsk 8. Ydrgig`clks

x2 -61 3 2 2

x0 -91 6 = 4

f3 1 3 1 1

f2 1 1 3 1

f0 1 1 1 3

Pkj Pkj 1 84 71 311

sg tkhks jks `kdig`gdotds csk`gchks cj rdomjðo hd ^ sko

lcykrds k gmucjds c `drk, sg ds csì, dotko`ds jc skju`gðo do jc tcbjc ds jc ðptglc y dj prk`dsk tdrlgoc. Pg ok ds csì sd `kotgouc Ycr.Bcs. ^ R 1 R 3 R 2 R 0

^ f3 f2 f0

3 1 1 1

x3 -01 0 = 4

x2 -61 3 2 2

x0 -91 6 = 4

f3 1 3 1 1

f2 1 1 3 1

f0 1 1 1 3

Pkj Pkj 1 84 71 311

Pg dxgstdo vcjkrds ≨ 1, pkr jk tcotk, `kotgouc dj prk`dsk.

Dndr`g`gk 0. (3 puotk)

Kbtço jc tcbjc prglcj hucj  y dj lkhdjk hucj hd lcxglgzc`gðo  hdj sgmugdotd lkhdjk>

Xcbjc prglcj/hucj

4

 

Toghch 0> Lçtkhk

sglpjdx y coãjgsgs hd hucjghch

Lctdlã`cs pcrc jks Odmk`gks

Qrglcj Hucj y3 y2 y0 ≨

x3

x2

x0

4 3 3 311

31 1 3 211

34 3 1 011

 

≤

21 01 41

Lkhdjk hucj hd lcxglgzc`g lcxglgzc`gðo. ðo. ^Lcx < 21y3 + 01y2 + 41y0 Pundtk c> 4y3 + y2 + y0 ≨ 311 31y3 + y0 ≨ 211 34y3 + y2 ≨ 011 y3, y2, y0 ≤ 1

Dndlpjk>

Pd cpjg`crã jks prgldrks pcsks hd jc ldtkhkjkmìc sglpjdx cj sgmugdotd lkhdjk hd QJ ^Lcx < x3 +0x2+4x0 Pundtk c> 2x3+x2+2x0 ≨ 4 x3 +2x2+x0 ≨ 4 @OO x3, x2 , x0 ≤ 1 Qcsk 3. @kovdrtgr jcs hdsgmucjhchds do gmucjhchds cj sulcrjds uoc vcrgcbjd hd fkjmurc.

Jcs vcrgcbjds hd fkjmurc sgdlprd sko pksgtgvcs. 2x3+x2+2x0 + f3 < 4 x3 +2x2+x0 + f2 < 4 Qcsk 2. Ds`rgbgr jc iuo`gðo kbndtgvk `klk uoc gmucjhch c `drk sulcohk jcs vcrgcbjds hd

fkjmurc `ko `kdig`gdotd `drk y `kosdrvcohk pksgtgvk dj `kdig`gdotd ^Lcx> ^Lcx - x3 -0x2 -4x0 +1f3+1f2 < 1

9

 

Toghch 0> Lçtkhk

sglpjdx y coãjgsgs hd hucjghch

Lctdlã`cs pcrc jks Odmk`gks

Ycrgcbjds

^

V3

V2

V0

f3

f2

PKJT@GÐO

Bãsg`cs ^

3

-3

-0

-4

1

1

1

Iuo`gðo kbndtgvk

f3

1

2

3

2

3

1

4

Rdstrg``gðo 3

f2

1

3

2

3

1

3

4

Rdstrg``gðo 2

Qcsk 8. Ydrgig`clks sg tkhks jks `kdig`gdotds csk`gchks cj rdomjðo hd ^ sko lcykrds k

gmucjds c `drk, sg ds csì, dotko`ds jc skju`gðo do jc tcbjc ds jc ðptglc y dj prk`dsk tdrlgoc. Pg ok ds csì, sd `kotgoþc. Ycrgcbjds

^

V3

V2

V0

f3

f2

PKJT@GÐO

^

3

-3

-0

-4

1

1

1

f3

1

2

3

2

3

1

4

f2

1

3

2

3

1

3

4

Bãsg`cs

Pg dxgstdo vcjkrds ≨ 1, pkr jk tcotk, `kotgouc dj prk`dsk.

=