Problemas Ao2

1. Una !"#$a %& 'a(#)*a *!"&a#a$ "#$na$ X/, n*$)a $!a# $&$ na$  "#x)! a. La $)&)n a(a *nn $ )n#$$  na$ na$  C$ X/  a !"#$a  $ !$ $)$ a$: AÑO

INSO O ;N/AS a#$?

1 2 3 4 5 6

2.4 5.9 15.5 27.8 35.9 38.1

SOLUCION: AÑO

INSO O ;N/AS a#$?  : 0.6663719343

600 400 200 0

K?

0

200

400

600

CU;A > /N>NCIA LINAL

Y:;+N>IN/ X = 64

>?

COJICIN/ > SION

=>*?@

800

1000

1200



0.81631607

:

81M

4. La *n'# n *!"anD CC $ &n 'a(#)*an !)an *n 10 a$  anPa  *a'a**)n D n'#)a!)n. La$ na$ $n *#*)n *n #a") D $ n*$a#) )n*#!na# a *a"a*)a  "#&**)n. La #n*)a  a !"#$a $ "#&na $) $ a$ na*)na$  *n$#&**)n  ))na "&)#a #$&a# &n (&n )n)*a#  a$ na$ an&a$  a !"#$a

a!o

"ons$r""iones en$as anlaes de de iiendas "" (%illones de (%illones ) dolares) 1 2.1 230 2 1.8 215 3 2.4 270 4 2.8 310 5 3.1 360 6 2.6 370 7 2.4 375 8 2.6 321 9 3 368

X@

Y@

4.41 3.24 5.76 7.84 9.61 6.76 5.76 43.38

A : 116,62 + 17,724

@ = 0,5602

en$as e N A a "ons$r""ion e iien as. * naona o%e bilders asso"iaon es%a e la inersion en "ons$r""ion de iiendas sera de 2,6 %illones A de 3,0 %illones &ara los dos a!os si#ien$es >.

iiendas (%illones )

a!o 8 9

de dolares) 2.6 3

321 368

B* C*D* *> EC* ; ;>F;FGH D* *H;B *H FF*HD;B *B D*

56.02I

) >*BGHD; ;B BFJCF*H*B >*JCH;B i. re"o%ne$daria s$ed e N liara el &ronos"o del insiso a) &ara &lanear na e&ansion de las ins$ala"iones Lse s re&es$a HG B* >*GM*HD; D*MFH;FGH 0,5602 *B; ;*L;DG D* 1 FF. EC* GD>F; K;*>B* ;>; M*LG>;> * >GHGBFG

;>; M*LG>;> * >GHGBFG B* C*D* G;> GM;> CH; >*J>*FGH GH*F; G> e el "oe"ien$e de

Y@ 52900 46225 72900 96100 129600 136900 140625 675250

XY 483 387 648 868 1116 962 900 5364

>

5. la &lan$a F es%a la de%anda se%anal de los %"os %a$eriales e ene en el inen$ario. *s$a es$diando no de ss "o%&onen$es, el > 5922. as 12 se%anas %as re"ien$es de de%anda &ara el > 5922 son H : 13 se%anas de%anda se%ana desia"ion (nidades) &ronos"os absol$a 1 2 3 4 5 6 7 8 9 10 11

169 227 176 171 163 157 213 175 178 158 188

190.67 191.33 170.00 163.67 177.67 181.67 188.67 170.33

-19.67 -28.33 -13.00 49.33 -2.67 -3.67 -30.67 17.67

12

169

174.67

-5.67

13

171

171.67

170.67 -170.33

se%ana

de%anda (nidades)

1 2 3 4 5 6

169 227 176 171 163 157

169 454 528 684 815 942

1 4 9 16 25 36

28561 51529 30976 29241 26569 24649

7

213

8 9 10 11 12

175 178 158 188 169

1491 1400 1602 1580 2068 2028 13761

49 64 81 100 121 144 650

45369 30625 31684 24964 35344 28561 388072

$o$al

xD

x@

a:186,62 b:-1,2238 A : -1,2238 + 186,62

D@

4. li"e el %e$odo de &ro%edios %oiles &ara &ronos"os a "or$o &lao, "on n &ro%edio de $res se%anas, &ara desarrollar &ara la se%ana 13 n &ronos"o de la de%anda del "o%&onen$e > 5922  > ara la se%ana 13 $ene%os n &ronos"o de 171,67

$!ana 1 2 3 4 5 6 7 8 9 10 11 12 13

!ana #n$* $)a*)n a($&a Q=0,25

17.24 -6.07 -2.84

26.15 BGCFGH ?12:170,76+0,25Q(188-170,76) ?12:175,07 ?13:175,07+0,25Q(169-175,07) ?13:173,55

7.Ko$el o&a"abana es n #ran o$el A "asino a orillas del la#o i"a"a. *l o$el es relaa%en$e neo, de dos a!os, A el #eren$e es$/ in$en$ando desarrollar n &lan &ara el &ersonal del de&ar$a%en$o de %an$ea%ien$o. *l #eren$e del o$el desea liar los dos a!os de da$os e a&are"en a "onna"in &ara &ronos"ar "on n %es de an"i&a"in la "andad de lla%adas &ara %an$eniendo

%eses (%eses 15-24) "on n%ero de &eriodos de 2,4,6 A 8 %eses de &ronos"o 4 %eses 6 %eses

2 %eses lla%adas &or %an$eni%ien$o

%es

desia"ion

&ronos"o absol$a

1

46

2

39

3

28

4

21

5

14

6

16

7

14

8

13

9

9

10

13

11

18

12

15

13

12

14

6

15 16

19 9

17

12

18

14

19

16

20

12

21

13

22

9

23

14

24

15

9 12.5 14 10.5 13 15 14 12.5 11 11.5

10 3.5 2 3.5 3 3 1 3.5 3 3.5 36 3.60

&ronos"o

12.75 13.00 11.50 11.50 13.50 12.75 13.50 13.75 12.50 12.00

desia"ion absol$a

6.25 4 0.5 2.5 2.5 0.75 0.5 4.75 1.5 3 26.25 2.63

&ronos"o

12.17 13.83 13.17 12.17 12.00 12.67 13.67 12.67 12.67 13.00

8 %eses

desia"ion absol$a

6.83 4.83 1.17 1.83 4.00 0.67 0.67 3.67 1.33 2.00 27.0 2.70

&ronos"o

desia"ion absol$a

6.50 4.13 0.63 1.00 2.88 0.88 0.50 3.63 1.00 2.63 23.8 2.38

b) Ee "andad de &eriodos &ro%ediados da "o%o resl$ado el error de &ronos"o %edio absol$o %as bao la "andad %as baa &ro%ediada es de 2,38 de %an$eni%ien$o

") OEe n%ero de &ro%ediado re"o%ienda s$ed Oore

se re"o%ienda $o%ar 2,28 de &ro%edio e nos da en 8 %eses &ara &oder desarrollar n &lan de %an$enien$o d) Cliando la "andad de &eriodos &ro%ediados e s$ed re"o%ienda. ronose el n%ero de lla%adas &ara %an$eni%ien$o &ara el %es si#ien$e (%es 25)

'25: 12+14+16+12+13+9+14+15S8

  '25:13,13 lla%adas &or %es %an$eni% ien$o 25 13.13

0.5 0.25 0.125 0.0625 0.03125 0.015625 0.0078125 0.00390625 0.001953125 0.0009765625 0.0004882813 0.0002441406 0.0001220703 6.103515625*-05 3.0517578125*-05 1.52587890625*-05 7.62939453125*-06 3.814697265625*-06 1.9073486328125*-06 9.5367431640625*-07 4.76837158203125*-07 2.38418579101562*-07 1.19209289550781*-07 5.96046447753906*-08

5.9605*-08 1.1921*-07 2.3842*-07 4.7684*-07 9.5367*-07 1.9073*-06 3.8147*-06 7.6294*-06 1.5259*-05 3.0518*-05 6.1035*-05 0.00012207 0.00024414 0.00048828 0.00097656 0.00195313 0.00390625 0.0078125 0.015625 0.03125 0.0625 0.125 0.25 0.5

13.75

6)a 50 45 40

30 25

'() : - 0.7752173913 + 26.231884 > : 0.3555149781

20 15 10 5 0

0

5

10

r$ 8i$le

58

15

20

25

30

;)desarrolle los &esos o "oe"ien$es de &ondera"ion a liarse en el &ronos"o de &ro%edios %oiles &onderados &ronos"o %es

lla%adas &or %an$eni%ien$o

2 %eses &ronos"o

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

46 39 28 21 13.999999 15.9999981 13.9999962 12.9999924 8.99998474 12.9999695 17.999939 14.9998779 11.9997559 5.99951172 18.9990234 8.99804688 11.9960938 13.9921875 15.984375 11.96875 12.9375 8.875 13.75 14.5

9.00 12.50 14.00 10.50 12.99 14.99 13.98 12.45 10.91 11.31

4 %eses

desia"ion absol$a

10.00 3.50 2.00 3.50 2.99 3.02 1.04 3.58 2.84 3.19 36 3.57

&ronos"o

12.75 13.00 11.50 11.50 13.50 12.74 13.49 13.72 12.44 11.88

6 %eses

desia"ion absol$a

6.25 4.00 0.50 2.49 2.49 0.77 0.55 4.85 1.31 2.62 25.82 2.58

&ronos"o

12.17 13.83 13.17 12.17 12.00 12.66 13.66 12.65 12.63 12.92

8 %eses

desia"i on absol$a

6.83 4.83 1.17 1.83 3.99 0.69 0.72 3.77 1.12 1.58 26.5 2.65

&ronos"o

desia"ion absol$a

= = = = = = = = = =

b) lise los &esos del insiso b) &ara &ronos"ar la "andad de ll%adas &ara el %an$enie%ien$o &ara el %es 25 de los da$os del &roble%a an$erior

18.9990234 0.018554 8.99804688 11.9960938 13.9921875 15.984375 11.96875 12.9375 8.875 13.75

6.50 4.13 0.63 0.99 2.86 0.90 0.45 3.73 0.78 2.19 23.2 2.32

46 39 28 21 14 16 14 13 9 13 18 15 12 6 19 9 12 14 16 12 13 9 14 15

0.5 0.25 0.125 0.0625 0.03125 0.015625 0.0078125 0.00390625 0.001953125 0.0009765625 0.0004882813 0.0002441406 0.0001220703 6.103515625*-05 3.0517578125*-05 1.52587890625*-05 7.62939453125*-06 3.814697265625*-06 1.9073486328125*-06 9.5367431640625*-07 4.76837158203125*-07 2.38418579101562*-07 1.19209289550781*-07 5.96046447753906*-08

5.960464478*-08 1.192092896*-07 2.384185791*-07 4.768371582*-07 9.536743164*-07 1.907348633*-06 3.814697266*-06 7.629394531*-06 1.525878906*-05 3.051757813*-05 6.103515625*-05 0.0001220703 0.0002441406 0.0004882813 0.0009765625 0.001953125 0.00390625 0.0078125 0.015625 0.03125 0.0625 0.125 0.25 0.5

13.75

50 45 40 35 30 25 20 15

'() : - 0.78434782 > : 0.3628475307

5 0

0

5

6)ar$ 8i$le

8 + 26.3043478373

10

15

20

25

30

9. Cna inds$ria %inera adiere, #randes "andades de "obre e se e%&lean en ss &rod"$os %an'a"$rados. a e%&resa es$/ desarrollando n sis$e%a de &rons"o &ara los &re"ios del "obre. Ka a"%lado los si#ien$es da$os is$ri"os a) li"e la saia"in e&onen"ial &ara &ronos"ar los &re"ios %ensales del "obre, "al"le "ales bieran sido los &rons"os &ara $odos los %eses de da$os is$ri"os "on T:0,1, T:0,3A T:0,5, si &ara $odas las T el &rons"o del &ri%er %es 'e de 99"en$aos de dlar

>*FG D* G* (USlibra)

M*B

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0.99 0.97 0.92 0.96 0.93 0.97 0.95 0.94 0.98 0.91 0.89 0.94 0.99 0.95 0.92 0.97

D*BF;FGH ;GHGBF G

0.99 0.99 0.99 0.98 0.98 0.97 0.97 0.97 0.97 0.97 0.96 0.96 0.95 0.96 0.96 0.95

D*BF;FGH ;GHGBFG

0.00 0.02 0.07 0.02 0.05 0.00 0.02 0.03 0.01 0.06 0.07 0.02 0.04 0.01 0.04 0.02 0.48 0.030

0.99 0.99 0.98 0.96 0.96 0.95 0.96 0.96 0.95 0.96 0.94 0.93 0.93 0.95 0.95 0.94

D*BF;FGH ;GHGBF G

0.99 0.99 0.98 0.95 0.96 0.94 0.96 0.95 0.95 0.96 0.94 0.91 0.93 0.96 0.95 0.94

D*BF;FGH ;L COK S;. AKSOLU/A

0.95

0.95

0

8

0.94

0.95

-0.01

9

0.98

0.95

0.03

10

0.91

0.96

-0.05

11

0.89

0.94

-0.05

12

0.94

0.93

0.01

13

0.99

0.91

0.08

14

0.95

0.94

0.01

15

0.92

0.96

-0.04

16

0.97

0.95

0.02

D*>*BFGH ;*BFGH ;