Aplicatii Mk

7/28/2019 Aplicatii Mk

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APLICA II

(67,0$5($,35(9,=,21$5($&(5(5,,

1. 2 ILUP FDUH GLVWULEXLH SURGXVH LQGXVWULDOH HVWLPHD] F YkQ] ULOH VDOH YRU FUHWH vQXUP WRDUHOHOXQLFXID GHFLIUDDFWXDO FDUHHVWHGHXP

6 VHFDOFXOH]HYkQ] ULOHFHVHHVWLPHD] DILRE LQXWHvQILHFDUHGLQWUHFHOHOXQLGDF VH

LDvQFRQVLGHUDUHLSRWH]DFUHWHULLFRQVWDQWHvQILHFDUHOXQ

REZOLVARE:

QSULPXOUkQGHVWHQHFHVDUV VHFDOFXOH]HUDWDGHFUHWHUHSHQWUXILHFDUHOXQ UDW FDUHYDILDFHHDL

'DF YkQ] ULOH ILUPHL YRU FUHWH FX R UDW SURFHQWXDO FRQVWDQW SHQWUX R SHULRDG 3 Lconsidernd X0 YkQ] ULOHvQSHULRDGDYkQ] ULOHvQSULPDOXQ YRUIL

X1 = X0 + 0X100

P= X0 (

100

P1+ )

6LPLODUYkQ] ULOHSHQWUXDGRXDOXQ YRUIL

X2 = X1 + 1X100P = X1 (

100P1+ ) = X0 ( 100P1+ )( 100P1+ ) =

= X0 (1 +100

P)2

3HQWUXOXQDWYkQ] ULOHYRUIL

Xt = X0 (1 +100

P)t

'DF vQFHOHWOXQLYkQ] ULOHYRUFUHWHFXRUDW &FXPXODW WUHEXLHVDWLVI FXW UHOD LD

Xt = X0 + 0X100

C= X0 (

100

C1+ ) (1+

100

P)t

= 1 +100

C

P = (100

C1+ )1/t- 1] 100

P = [( 1+0,45 )1/12 - 1] 100 = 3,14

X1 = X0 (100

P1+ ) = 23.500 (1+ 0,0314) = 24.237,9 u.m.

6LPLODUVHYRUFDOFXODYkQ] ULOHSHQWUXWRDWHFHOHODOWHOXQL

Luna 9kQ] ULHVWLPDWHXP

0 23.500

1 24237,90

2 24998,97

3 25783,94

4 26593,555 27428,59

6 28289,85

7 29178,15

8 30094,34

9 31039,30

10 32013,93

11 33019,17

12 34055,97


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2. )LUPD(DREVHUYDWF ODFUHWHUHDSUH XOXLSURGXVXOXL t de la 250 u.m. la 300 u.m.,YkQ] ULOH OXQDUH V-au redus de la 2500 OD EXF L I U V H[LVWH R DOW H[SOLFD LH D DFHVWHLreduceri.

6HGRUHWHV VHHVWLPH]HHODVWLFLWDWHDFHUHULLvQIXQF LHGHSUH vQDFHVWLQWHUYDO

REZOLVARE:

(ODVWLFLWDWHDFHUHULLTvQIXQF LHGHSUH SVHGHILQHWHDVWIHOe = -

p/p

q/q

'DUFRQVLGHUkQGXQDQXPLWLQWHUYDOvQFDUHVHPRGLILF SUH XULOHLFDQWLW LOHFHUXWHVHYDGHILQLXQcoeficient de elasticitate mediu al intervalului:

e = -p/p

q/q

, unde:

12 ppp = 12 qqq =

2

ppp

2

qqq

12

12

+=

+=

Elasticitatea medie a cererii devine:

12

12

qq

ppe

++

= .12

12

pp

qq

n cazul produsului t IDEULFDWGHILUPD(VHRE LQH

25002250

250300e

++

= . 5789.0250300

25002250=

3. SeSRDWHFRQVLGHUDDGHFYDW GHFL]LDILUPHLGLQSUREOHPDDQWHULRDU GLQSXQFWGHYHGHUHDOPD[LPL] ULLYHQLWXULORU"

REZOLVARE:

9HQLWXULOHvQDLQWHGHPRGLILFDUHDSUH XULORU000.6252502500pq 11 == u.m.

9HQLWXULOHGXS PRGLILFDUHDSUH XULORU000.6753002250pq 22 == u.m.

5H]XOW F GLQSXQFWGHYHGHUHDOPD[LPL] ULYHQLWXULORUFDUHQXFRLQFLGHFXPD[LPL]DUHDSURILWXOXLGHFL]LDHVWHDGHFYDW

Q]RQHOHFXUEHLFHUHULLvQFDUHFHUHUHDHVWHLQHODVWLF H YDULD LHL SUH XOXL vL FRUHVSXQGH RPRGLILFDUH D FDQWLW LLFHUXWH vQWU-R SURSRU LH PDL PDUH i din acest punct de vedere decizia deUHGXFHUHDSUH XOXLHVWHFRUHFW

9HQLWXOPD[LPVHRE LQHvQSXQFWXOvQFDUHHODVWLFLWDWHDHVWHXQLWDU H


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Pentru r = 0,25

2550q1 =* &UHWHUHD ( )r1*qrq t1 = t-1 = ( )25.01255025.0 0 = 637,5 buc.


2650q3

=*

&UHWHUHD ( )r1*qrq t3 = t-1 = ( )25.01265025.0 2 = 372,7 buc.2700q4 =*

&UHWHUHD ( )r1*qrq t4 = t-1 = ( )25.01270025.0 3 = 284,8 buc.'DF VHFRQVLGHU RUDW GHSHQHWUDUHGHFHUHUHDWRWDO SHQWUXQRXOSURGXVDOILUPHLvQ

cele patru perioade considerate este:

=4

1

Tq &UHWHUHD 5,17828,2847,3725,4875,637qt =+++= buc.

Pentru r = 0,50

2550q1 =* &UHWHUHD ( )r1*qrq t1 = t-1 = ( )50.01255050.0 0 = 1275 buc.

2600q2 =* &UHWHUHD ( )r1*qrq t2 = t-1 = ( )50.01260050.0 1 = 650 buc.

2650q3 =* &UHWHUea ( )r1*qrq t3 = t-1 = ( )50.01265050.0 2 = 331,25 buc.


3HQWUXRUDW GHSHQHWUDUHGHFHUHUHDWRWDO HVWH

=4

1

Tq CrHWHUHD 242575,16825,3316501275qt =+++= buc.

Pentru r= 0,75

2550q1 =* &UHWHUHD ( )r1*qrq t1 = t-1 = ( )0751255075.0 0 = 1912,5 buc.


2650q3 =*

&UHWHUHD ( )r1*qrq t3 = t-1 = ( )75.01265075.0 2 = 124,2 buc.2700q4 =*

&UHWHUHD ( )r1qrq t4 = * t-1 = ( )75.01270075.0 3 = 31,6 buc.3HQWUXRUDW GHSHQHWUDUHGHFHUHUHDWRWDO HVWH

=4

1

Tq &UHWHUHD 8,25556,312,1245,4875,1912qt =+++= buc.

3URILWXOVHGHWHUPLQ vQ IXQF LHGHFDQWLW LOHHVWLPDWHvQILHFDUHSHULRDG L SURILWXOXQLWDUdependent de rata de penetrare.

Considerndpf iSURILWXOXQLWDULqIcantitatea acumuODW SURILWXOSHQWUXFHOHSDWUXSHULRDGHde timp va fi:


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3UH SI

( )

( )

( ) .m.u900.2138,2847,1497120qpfPf

.m.u724.1797,3721125120qpfPf

.m.u000.1355,4875.637120qpfPf

.m.u500.765.637120qpfPf

44

33

22

11

=+===+===+==

===

3HQWUXRUDW GHSHQHWUDUHGHSURILWXOWRWDOvQFHOHSDWUXSHULRDGHFRQVLGHUDWHYDIL

=+++==4

1

iT .m.u124.605900.213724.179000.135500.76PfPf

3UH SI

( )

( )

( ) .m.u500.24275,16825,2256100qpfPf

.m.u625.22525,3311925100qpfPf

.m.u500.1926501275100qpfPf

.m.u500.1271275100qpfPf

44

33

22

11

=+===+==

=+=====

3HQWUXRUDW GHSHQHWUDUHGHSURILWXOWRWDOSHQWUXFHOHSDWUXSHULRDGHFRQVLGHUDWHYDIL.m.u125.788500.242625.225500.192500.127PfPf

4

1

iT =+++==

3UH SI

( )

( )

( ) .m.u464.2046,312,252480qpfPf

.m.u936.2012,124240080qpfPf

.m.u000.1925,4875,192580qpfPf

.m.u000.1535,191280qpfPf

44

33

22

11

=+===+==

=+=====

3HQWUXRUDW GHSHQHWUDUHGHSURILWXOWRWDOSHQWUXFHOHSDWUXSHULRDGe considerate va fi:

.m.u400.751464.204936.201000.192000.153PfPf4

1

iT =+++== &RPSDUkQGSURILWXULOHRE LQXWHvQFHOHWUHLFD]XULVHSRDWHDSUHFLDF YDORDUHDFHDPDLPDUH

DDFHVWXLDFRUHVSXQGHSUH XOXLGHXPLUDWHLGHSHQHWUDUHDSLH HLGH

PROBLEME PROPUSE:

P1:2ILUP GLVWULEXLWRDUHGHSURGXVHLQGXVWULDOHHVWLPHD] F YkQ] ULOHVDOHYRUFUHWHvQXUP WRDUHOHOXQLFXID GHFLIUDDFWXDO FDUHHVWHGHPLOXP

6 VHFDOFXOH]HYkQ] ULOHFHVHHVWLPHD] DILRE LQXWHvQILHFDUHGLQWUHFHOHOXQLGDF VH

LDvQFRQVLGHUDUHLSRWH]DFUHWHULLFRQVWDQWHvQILHFDUHOXQ

P2:)LUPD=DREVHUYDWF ODFUHWHUHDSUH XOXLSURGXVXOXL t de la 310 u.m. la 350 u.m.,YkQ] ULOH OXQDUH V-DX UHGXV GH OD OD EXF L I U V H[LVWH R DOW H[SOLFD LH D DFHVWHLreduceri.


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Criteriu 3RSXOD LDWRWDO Consumatori

&/$6 62&,$/ $,QIHULRDU 520 80B. Medie 1.440 152

&6XSHULRDU 2.040 168

VRSTA

1. < 30 ani 500 1242. 31 50 ani 1.360 1403. >50 ani 2.140 136

6 VHGHWHUPLQHFDUHYDILFULWHULXOGHVHJPHQWDUHDOHVXWLOL]kQGPHWRda BELSON.

REZOLVARE:

0HWRGD %(/621 vL SURSXQH V HVWLPH]H SXWHUHD GLVFULPLQDWRULH D GLIHULWHORU YDULDELOHGLKRWRPLFHYDULDELOHFHSRWDYHDGRDUVW ULDOWHUQDWLYHH[IHPHLE UED LFXDMXWRUXOF URUDVHvQFHDUF H[SOLFDUHDFRPSRUWDPHQWXOXLXQHLSRSXOD LLGDWHH[FRQVXPDWRULQRQFRQVXPDWRUL

3HQWUXF vQGLVWULEX LDSHUVRDQHORUvQIXQF LHGHFODVDVRFLDO LYkUVW SUH]HQWDW DQWHULRUDXIRVWFRQVLGHUDWHFkWHVHJPHQWHDFHVWHDWUHEXLHV ILHJUXSDWHH[;11= clasa medie LQIHULRDU L;12= FODVDVXSHULRDU ;21= 50 ani ).

9RP FDOFXOD vQ WDEHOXO XUP WRU SURSRU LLOH SH FDUH OH GH LQ FRQVXPDWRULL vQ WRWDOXOSHUVRDQHORUFHSUH]LQW RDQXPLW FDUDFWHULVWLF

Criteriu % Consumatori

&/$6$62&,$/ $,QIHULRDU (80 / 520) x 100 = 15,38 (>10)B. Medie (152 / 1440) x 100 = 10,56 (>10)&6XSHULRDU (168 /2040) x 100 = 8,23 (10)2. 31 50 ani (140/1360) x 100 = 10,29 (>10)3. >50 ani (136/2140) x 100 = 6,36 (


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Criteriu 3RSXOD LHWRWDO Consumatori % Consumatori

VENITURI

(R) 3040 520 17,10(M) 3015 403 13,36

(A) 3945 277 7,02

ZONA GEOGR.(N) 3550 345 9,71

(C) 2285 456 19,95(S) 4165 399 9,57

9567 (T) 2840 339 11,93(A) 5575 751 13,47

(V) 1585 110 6,94

SEX(F) 4910 510 10,38(B) 5090 690 13,55

67$5(&,9,/ (S) 7100 819 11,53

(C) 2900 381 13,13

'LVWULEX LDvQFDWHJRULLGLKRWRPLFHHVWH

Criteriu 3RSXOD LDWRWDO Consumatori

VENITURIR+M 6055 923

A 3945 277

ZONAN+S 7715 744

C 2285 456

VRSTAT+V 4425 449

A 5575 751

SEXF 4910 510

B 5090 690

67$5(&,9,/ S 7100 819

C 2900 381

3XWHUHDGLVFULPLQDQW DGLIHULWHORUFULWHULLVHFDOFXOHD] DVWIHOVENIT:I 923 0,12 x 6055 I = I 277 0,12 x 3945 I = 196,4

=21 I 744 0,12 x 7715 I = I 456 0,12 x 2285 I = 181,8

9567 I 449 0,12 x 4425 I = I 751 0,12 x 5575I = 82

SEX:

I 510 0,12 x 4910 I = I 690 0,12 x 5090 I = 79,2

67$5(&,9,/


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PB SRSXOD LDORFDOLW LL%DA GLVWDQ DGLQWUHORFDOLWDWHD;LORFDOLWDWHD$DBGLVWDQ DGLQWUHORFDOLWDWHD;LORFDOLWDWHD%

31

n cazul concret prezentat:PG = 56.900PC = 41790

DG = 61DC = 87Aplicnd formula lui Reilly:

C

G

V

V=

2

61

87

41.790

56.900

= 2,76

$FHDVWDvQVHDPQ F ORFDOLWDWHD* YLQGHGHRUL PDL PXOW ORFDOLW LL LQWHUPHGLDUH ;GHFkWORFDOLWDWHD&5H]ROYkQGVLVWHPXOGHHFXD LL:

C

G

V

V= 2,76

VG + VC = 15H]XOW F 9GL9C DGLF ORFDOLWDWHD*DWUDJHGLQYkQ] ULLDUORFDOLWDWHD&

atrage 26,6%.

2. 2ILUP GRUHWHV GHOLPLWH]HDULDGHDWUDF LHFRPHUFLDO DXQXLRUD;DVXSUDXQXLQXP UdH ORFDOLW LPDL LPSRUWDQWHGLQ]RQHOHvQYHFLQDWHvQ VFRSXOGHD GHFLGH SkQ ODFHGLVWDQ GHRUDXO;YDSXWHDH[WLQGHGLVWULEX LDSURGXVHORUVDOH

,QIRUPD LLOHGHVSUHSRSXOD LDLGLVWDQ HOHvQWUHORFDOLW LYRUILSUH]HQWDWHvQWDEHOXOXUP WRU

LocaOLW L 3RSXOD LH(nr. loc.)

'LVWDQ DID GH;NP

X 320.000 -A 225.000 100

B 400.000 140C 270.000 165D 150.000 190

REZOLVARE:3HQWUXDGHOLPLWDDULDGHDWUDF LHFRPHUFLDO DXQXLRUDVDXFHQWUXFRPHUFLDOVHSRDWHXWLOL]D

OHJHDJUDYLWD LHLFomerciale a lui ReillyXWLOL]DW LvQSUREOHPDDQWHULRDU

B

A

V

V=

2

A

B

B

A

D

D

P

P, unde VA = VB

/LPLWHOHDULLORUFRPHUFLDOHVHGHWHUPLQ SULQSUHFL]DUHDSXQFWXOXLvQFDUHDWUDF LDFHORU

GRX FHQWUHFRPHUFLDOHHVWHLQGLIHUHQW DGLF SXQFWXOvQFDUHVXQWDWUDVHDFHOHDLYkQ] ULQDFHVWHFRQGL LLDSOLFkQGIRUPXODOXL5HLOO\YRPRE LQH

1 =2

A

B

B

A

D

D

P

P 1 =

A

B

B

A

D

D

P

P

DB = DAA

B

P

P DB + DA = DA

A

B

P

P+ DA


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DB + DA = DA 1+P

P

A

B

'DF VHFRQVLGHU 'TGLVWDQ DWRWDO vQWUH$L%DGLF

DT = DA 1+P

P

A

B

DA =

A

B

T

P

P+1

D

$VHP Q WRUVHYDFDOFXODL'B

DB =

B

A

T

P

P

D

+1

Aceste expresii reprH]LQW GLVWDQ HOH GLQWUH ORFDOLW LOH $ L % L SXQFWXO GH LQGLIHUHQ 8QLQGVXFFHVLYSXQFWHOHGHLQGLIHUHQ VHSRDWHGHOLPLWDDULDGHLQIOXHQ DXQXLFHQWUXFRPHUFLDO

DXA =

0003200002251

100

..+

= 54,39 km

DXB =0003200004001

140

..+= 66,10 km

DXC =0003200002701

165

..+= 86,00 km

DXD =0003200001501

190

..+= 112,78 km

3. 6 VHFDOFXOH]HSURFHQWXOYkQ] ULORUFXDP QXQWXOSHFDUHRUDXO+OHSLHUGHvQIDYRDUHDRUDXOXL6WLLQGGLVWDQ DGLQWUHFHOHGRX RUDHHVWHGHNPLDUSRSXOD LLOe lor sunt de 127.800

ORFXLWRULSHQWUX+LORFXLWRULSHQWUX6

REZOLVARE:

Se poate utiliza formula lui Converse:

B

A

V

V=

24

DP

P

B

A, unde:

VAYkQ] ULOHDWUDVHGHORFDOLWDWHD$VB YkQ] ULOHDWUDVHGHORFDOLWDWHa BPA SRSXOD LDORFDOLW LL$PB SRSXOD LDORFDOLW LL%

DGLVWDQ DGLQWUHORFDOLWDWHD$LORFDOLWDWHD%$SOLFkQGIRUPXODvQFD]XOSUREOHPHLGDWHVHRE LQH

S

H

V

V=

2

94

4

800127

800653

.

.= 0,009

QFRQFOX]LHGLQYkQ] ULOHFXDP QXQWXOGLQRUDXO+VHUHDOL]HD] vQ6PROBLEME PROPUSE:

P1: 6 VH FDOFXOH]H SRQGHUHD YkQ] ULORU DWUDVH GH GRXD RUDH ; L


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REZOLVARE:

6H YD OXD vQ FRQVLGHUDUH OLPLWDUHD LQYHVWL LHL FDUHQX SHUPLWH ODQVDUHD vQDQXO XUP WRU Dtuturor celor 10 produse.

AcHDVWDSUHVXSXQHF ILUPDYDWUHEXLV DOHDJ DFHOHSURGXVHFDUHYRUDYHDUHQWDELOLWDWHDFHDPDLPDUHUDSRUWDW ODLQYHVWL LDHIHFWXDW Rata medie de rentabilitate:

i

Iiii

I

Cqpr =

, n care:ri = rata medie de rentabilitate a produsului ipi = prH XOSURGXVXOXLLqiFDQWLWDWHDFHUXW DQXDOGLQSURGXVXOLCi = costul total al produsului iIiLQYHVWL LDFRUHVSXQ] WRDUHSURGXVXOXLL

9DORULOHFHUHULLSUH XOXLLFRVWXULORUVXQWFXQRVFXWH

,QYHVWL LDGHUHDOL]DWSHQWUXILHFDUHSURGXVVHHVWLPHD] DILSURSRU LRQDO FXFRVWXULOHLGHDFHHDVHYDFDOFXODSURSRU LDILHF UXLSURGXVvQFRVWXOWRWDO$VWIHOSURSRU LLOHRE LQXWHvQFHHDFHSULYHWHFRVWXOWRWDOYRUILDSOLFDWHODLQYHVWL LDWRWDO GHXPGXS FDUHVHpoate

FDOFXODUDWDPHGLHGHUHQWDELOLWDWHDILHF UXLSURGXV

ProdusCost

(u.m.)Cost(%)

,QYHVWL LH(u.m.)

Rata

UHQWDELOLW LL

A 2.750.000 16,18 1.132.600 0,27B 3.650.000 21,47 1.502.900 0,23C 100.000 0,59 41.300 0,60D 1.500.000 8,82 617.400 0,081E 1.442.000 8,48 593.600 0,22F 745.000 4,38 306.600 0,016G 2.100.000 12,35 864.500 0,13

H 870.000 5,12 385.400 0,084I 3.000.000 17,65 1.235.500 0,15J 843.000 4,96 347.200 0,07

TOTAL 17.000.000 100 7.000.000 -

n continuare, se vor ordona produVHOHvQRUGLQHDGHVFUHVF WRDUHDUDWHLGHUHQWDELOLWDWHLVHYRUDOHJHDFHOHDFDUHDXRUHQWDELOLWDWHPDLPDUHUDSRUWDW ODLQYHVWL LDHIHFWXDW

ProdusRata

UHQWDELOLW LL,QYHVWL LH ,QYHVWL LD

DFXPXODW

C 0,60 41.300 41.300

A 0,27 1.132.600 1.173.900B 0,23 1.502.900 2.676.800E 0,22 593.600 3.270.400I 0,15 1.235.500 3.577.000G 0,13 864.500 4.812.500H 0,084 385.400 5.677.000D 0,081 617.400 6.035.400J 0,07 347.200 6.652.600F 0,016 306.600 7.000.000


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( ) ( ) ( )

.m.u657.811.9

1,1

11

1,1

1

1,1

1

1,1

1

000.250.6

000.000.101,1

1

1,1

1

1,1

1

1,1

1000.250.6000.000.10

10,01

000.250.6

10,01

000.250.6

10,01

000.250.6

10,01

000.250.6000.000.10VAN

4

432

432A

=

+

+=

++++

=+

++

++

++

+=

( ) ( ) ( )

.m.u111.921.5

1,1

1

1

1,1

1

1,1

1

1,1

1

000.600.6

000.000.151,1

1

1,1

1

1,1

1

1,1

1000.600.6000.000.15

10,01

000.600.6

10,01

000.600.6

10,01

000.600.6

10,01

000.600.6000.000.15VAN

4

432

432B

=

+

+=

++++=

=+

++

++

++

+=

6HGHFLGHUHDOL]DUHDXQXLSURLHFWWUDQVSXQHUHDOXLvQSUDFWLF DWXQFLFkQG9$1HVWHSR]LWLY QFRQVHFLQ DWkWSURGXVXO$FkWLSURGXVXO%VHSRWUHDOL]D'DF YDWUHEXLV DOHJHPXQXOGLQFHOHSURGXVHDWXQFLVHYDRSWDSHQWUXDFHODFXRYDORDUHDFWXDOL]DW QHW PDLPDUHGHFLSURGXVXO$YDILODQVDWSHSLD

5DWDLQWHUQ GHUHQWDELOLWDWHDXQXLSURGXVHVWHDFHDUDW SHQWUXFDUHYDORDUHDDFWXDOL]DW QHW HVWHQXO Pentru produsul A:

( ) ( ) ( )

++

++

++

++=

4A

3A

2AA r1

1

r1

1

r1

1

r1

1000.250.6000.000.100

rA

= 50%

Pentru produsul B:

( ) ( ) ( )

++

++

++

++=

4B

3B

2BB r1

1

r1

1

r1

1

r1

1000.600.6000.000.150

rB = 27,5%

&RQIRUPFULWHULXOXL5,5VHYDGHFLGHGHDVHPHQHDvQIDYRDUHDODQV ULLSHSLD DSURGXVXOXL$

PROBLEME PROPUSE:

P1:2ILUP DFRQFHSXWWUHLSURGXVHQRLXUPkQGV GHFLG ODQVDUHDSHSLD DXQXLVLQJXU

SURGXVvQSHULRDGDLPHGLDWXUP WRDUH3HQWUXDFHDVWDDUHDOL]DWRVHULHGHDQFKHWHGHSLD vQVFRSXOFXQRDWHULLRSLQLHLFRQVXPDWRULORUDVXSUDSURGXVHORU2GDW RE LQXWH UH]XOWDWHOH DFHVWRU DQFKHWH ILUPD D I FXW R DQDOL] L D VWDELOLW R LHUDUKLH DRELHFWLYHORUSRVLELOGHUHDOL]DW$FHVWHRELHFWLYHVHUHIHU vQSULQFLSDOODSURILWODFRWDGHSLD FHXUPHD] DILGH LQXW LODLPDJLQHDILUPHL

'DWRULW H[SHULHQ HLDQWHULRDUHSHFDUHRSRVHG ILUPDvQODQVDUHDQRLORUSURGXVHVHSRDWHUHDOL]DRHVWLPDUHDSURILWXOXLDWHSWDWSHQWUXILHFDUHSURGXVvQSHULRDGDLPHGLDWXUP WRDUHYDORULFHVXQWUHGDWHvQWDEHOXOXUP WRU


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q FDQWLWDWHDGHSURGXVUHDOL]DW p SUH XOXQLWDU6 VHGHWHUPLQHSUH XOFHYDSHUPLWHPD[LPL]DUHDSURILWXOXLDQXDODOILUPHL

REZOLVARE:

3URILWXOVHSRDWHGHWHUPLQDFDGLIHUHQ vQWUHYHQLWXULOHDQXDOHDOHILUPHLLFKHOWXLHOLOHWRWDOH

ale acesteia:

Pf= VT CT, n care:

Pf profitul anual al firmei;

VT veniturile totale anuale ale firmei;

CT cheltuielile totale anuale ale firmei.

Veniturile totale ale firmei pot fi determinate ca SURGXV vQWUH SURGXF LD RE LQXW L SUH XOacesteia:

VT = p x q = p(175.000 300p) = 175.000p 300p2

&KHOWXLHOLOHWRWDOHDQXDOHDOHILUPHLVHRE LQvQVXPkQGFRVWXULOHIL[HFXFHOHYDULDELOHCT = 150.000 + 15q = 150.000 + 15(175.000 300p) = =2.775.000 4.500p

Profitul anual al firmei:

Pf = 300p2 + 179.500p 2.775.0003UH XOFDUHPD[LPL]HD] SURILWXOVHYDRE LQHGHULYkQGIXQF LDSURILWXOXLLHJDOkQGFX]HUR

0=dp

dPf

179.000 + 600p = 0 => p = 299,16 u.m.

3. Firma UNED SA areXQDFWLYGHPLOLRDQHXP6HFRQVLGHU F ILUPDSURGXFHLYLQGHXQVLQJXUSURGXVSURGXVFHSUHVXSXQHXQFRVWIL[DQXDOPLOLRDQHXPLXQFRVWYDULDELOXQLWDU GH XP 6 VH GHWHUPLQH SUH XO GH YkQ]DUH FH YD SHUPLWH DFHVWHL ILUPH V RE LQ RUHQWDELOLWDWHHFRQRPLF DQXDO GHSHQWUXXQULWPDOSURGXF LHLLYkQ] ULLQRUPDOGHXQLW LIL]LFHDQXDO

REZOLVARE:

5HQWDELOLWDWHDHFRQRPLF HVWHUHQWDELOLWDWHDJHQHUDW GHDFWLYHGHFLUDSRUWXOvQWUHSURILWXOILUPHLLvolumul activului :

20,0000.000.000.1

)000.500360000.000.120(p000.500re

Activ

CosturiVeniturire

=+

=

=

p = 1.000 u.m.

4. &HSUH DU WUHEXLV IL[H]HILUPDGLQSUREOHPDDQWHULRDU GDF ODILQDQ DUHDDFWLYLW LLVDOHSDUWLFLS vQSURSRU LLHJDOHFDSLWDOXOSURSULXLFHOvPSUXPXWDWSHQWUXDRE LQHRUHQWDELOLWDWHILQDQFLDU GHvQFRQGL LLOHvQFDUHUDWDGREkQ]LLSHQWUXFDSLWDOXOvPSUXPXWDWHVWHGH


31/49


32/49


33/49

Nc = 1010

100

Q

q== comenzi pe an

&RQVLGHUkQGDQXOFRPHUFLDOGHGH]LOHQXP UXOGH]LOHvQWUHGRX UHDSURYL]LRQ ULYDIL

NR = 36=10

360zile

0 ULPHDPHGLHDVWRFXOXLYDIL15

2

1010

2

QSS S =+=+= PDLQLGHVS ODW

&RVWXOWRWDOYDILXUP WRUXO

=)2

Q+S(c+

Q

qc=C SsrT 10.000 x 10+20.000 x 15 = 400.000u.m./an

2. Canalul prin care se distribuie un anumit produs este format din 4 intermediari, fiecare

GLQWUHHLIL[kQGSUH XOGHYkQ]DUHSULQDSOLFDUHDXQXLSURFHQWGHDVXSUDSUH XOXLGHFXPS UDUHDOSURGXVXOXL'DF SUH XOFXFDUHSURGXF WRUXOYLQGHSURGXVXOUHVSHFWLYSULPXOXLLQWHUPHGLDUHVWHde 200 u.m., ce pUH YDSO WLFRQVXPDWRUXOSHQWUXSURGXVXOFRQVLGHUDW"

REZOLVARE:

3UH XOLQWHUPHGLDUXOXLQU31=200(1+0,20) =240 u.m.3UH XOLQWHUPHGLDUXOXLQU32=240(1+0,20) =288 u.m.3UH XOLQWHUPHGLDUXOXLQU33=288(1+0,20)=345,6 u.m.3UH XOLQWHUPHGLDUXOXLnr.4 : P4=345,6(1+0,20)= 414,72 u.m.Sau P4 = 200(1 + 0,20)

4= 414,72 u.m.

3. 3kQ D DMXQJH ODFRQVXPDWRUXQSURGXV XUPHD] XQFDQDO IRUPDW GLQ LQWHUPHGLDULILHFDUHGLQ HLDSOLFkQG ODSUH XO GH FXPS UDUHDO SURGXVXOXL'DF SURGXF WRUXO GRUHWH FDSUH XOGHYkQ]DUHILQDOODFRQVXPDWRUV ILHGHXPFHSUH YDWUHEXLV DSOLFHODYkQ]DUHD

F WUHSULPXOLQWHUPHGLDU"

REZOLVARE:

3UH XOGHYkQ]DUHF WUHFRQVXPDWRU353UH XOGHYkQ]DUHDOSURGXF WRUXOXL30P5 = P0(1+0,18)

5=> P0 = 800/1,18

5= 349,69 u.m.

PROBLEME PROPUSE:

P1: )LUPD&QHFHVLW DQXDOXQLW LGHFRPSRQHQWH;$SHQWUXPRQWDMXOURER LORUGH FXU HQLH )LHFDUH FRPSRQHQW FRVW XP L SHQWUX ILHFDUH FRPDQG HIHFWXDW ILUPD

SO WHWHXP&RVWXOVWRF ULLunei componente pe timp de un an este de 300 u.m., excluzndcosturile financiare. Costul de oportunitate al capitalului investit n stocuri este de 10%/an. Stocul

GHVHFXULWDWHVDXVLJXUDQ HVWHGHFRPSRQHQWH6 VHGHWHUPLQHa) P ULPHDRSWLP DFRmenzii;b) QLYHOXOPHGLXDOVWRFXOXLvQXQLW LIL]LFHc) QXP UXOGHFRPHQ]LDQXDOHd) costul anual de reaprovizionare;e) costul anual de stocare;f) costul total anual.


34/49

P2: Firma L are ca obiect de activitate vnzarea-FXPS UDUHDGHE UFLFXPRWRUQILHFDUHan cXPS U GLQ VWU LQ WDWH L YLQGH vQ LQWHULRUXO ULL GH DVWIHO GH E UFL &RVWXO JHVWLRQ ULLILHF UHLFRPHQ]LHVWHGHXPLFRVWXOVWRF ULLHVWHGHXPDQEDUF

Care va fi volumul optim al comenzii?

32/,7,&$35202 ,21$/

1. O soFLHWDWH FRPHUFLDO GRUHWH V UHDOL]H]H R FDPSDQLH SXEOLFLWDU vQ VFRSXO FUHWHULLYkQ] ULORU XQXL QRX VRUWLPHQWGH FRQIHF LL 3HQWUX DFHDVWD VRFLHWDWHD D UHDOL]DW R DQFKHW SHXQHDQWLRQGHGHSHUVRDQH

$QFKHWDVHED]HD] SHRVHULHGHYDULDELOHGHVFULSWLYHDOHSRSXOD LHLVH[YkUVW SUHIHULQ HYHQLW VLWXD LH SURIHVLRQDO L PHGLX GH UHHGLQ Q XUPD DQFKHWHL V-DX RE LQXW XUP WRDUHOHUH]XOWDWHvQFHHDFHSULYHWHFRQVXPXOSURGXVXOXL

9$5,$%,/ 3238/$ ,( CONSUMATORI

SEX

% UED L 2300 850Femei 2700 950

9567 15 24 ani 1080 190

25 44 ani 1730 870

45 64 ani 1440 560

DQLLSHVWH 750 18035()(5,1 (Stil modern 1500 926

Stil clasic 3050 684

Stil sport 450 190

VENIT

1.700.000 1.900.000 60 15

1.500.000 1.700.000 270 1261.300.000 1.500.000 2350 1023

1.100.000 1.300.000 1410 519

900.000 1.100.000 910 81

6,78$ ,(352)(6,21$/

Activitate pe cont propriu 490 281

$FWLYLWDWHVDODULDW 1520 452Gospodine 1280 351

RPHUL 520 1626WXGHQ L 630 380Pensionari 560 174

MEDIURural 1140 320

Urban < 500.000 loc 1680 420

Urban > 500.000 loc 2180 1060

TOTAL 5000 1800

6 VHGHWHUPLQHDXGLHQ DUHSUH]HQWDWLY WLSDFDPSDQLHLSXEOLFLWDUHLIDFWRULLH[SOLFDWLYLDLconsumului noului produs.


35/49

REZOLVARE:

1) Se va calcuODSHQWUXSURGXVXOFRQVLGHUDWUDWDGHSHQHWUDUHDSLH HL

100xP

CW

i

ii = , unde:

WiUDWDGHSHQHWUDUHDSLH HLVDXGHFRQVXPPHGLXCi = consumatorii produsului

PiSRSXOD LDFRQVLGHUDW $FHDVW UDW VHYDFDOFXODSHQWUXILHFDUHYDULDELO LSHQWUXILHFDUHJUXS VHJPHQWDOSRSXOD LHLconsiderate.

9$5,$%,/ RATA DE CONSUM

SEX

% UED L 39,96Femei 35,18

9567 15 24 ani 17,59

25 44 ani 50,29

45 64 ani 38,89

DQLLSHVWH 24,0035()(5,1 (Stil modern 61,73

Stil clasic 22,42

Stil sport 42,22

VENIT

1.700.000 1.900.000 25,00

1.500.000 1.700.000 60,00

1.300.000 1.500.000 43,53

1.100.000 1.300.000 36,81

900.000 1.100.000 8,90

6,78$ ,(352)(6,21$/

Activitate pe cont propriu 57,35

$FWLYLWDWHVDODULDW 29,74Gospodine 27,42

RPHUL 31,156WXGHQ L 60,32Pensionari 31,07

MEDIU

Rural 28,07

Urban < 500.000 loc 25,00

Urban > 500.000 loc 48,62

TOTAL 36,00

2) Q FDGUXO ILHF UHL JUXSH GH YDULDELOH VH YD DOHJH FHD PDL PDUH UDW GH SHQHWUDUH D SLH HLSegmentul corHVSXQ] WRU HVWH FRQVLGHUDW UHSUH]HQWDWLY SHQWUX JUXSD FRQVLGHUDW $FHVWXLsegment i se va atribui valoarea 1.

3) QLQWHULRUXOILHF UHLJUXSHGHYDULDELOHVHYRUFRPSDUDWRDWHFHOHODOWHVHJPHQWHFXVHJPHQWXOFRQVLGHUDWUHSUH]HQWDWLYvQFHHDFHSULYHWHFRQsumul produsului.


36/49

$FHDVW FRPSDUD LHVHYDIDFHVXEIRUPDXQXLUDSRUWvQWUHUDWDVHJPHQWXOXLLLUDWDVHJPHQWXOXLreprezentativ.

9$5,$%,/ RATA DE

CONSUM&203$5$ ,(

SEX

% UED L 39,96 1,0Femei 35,18 0,95

9567 15 24 ani 17,59 0,35

25 44 ani 50,29 1,0

45 64 ani 38,89 0,77

DQLLSHVWH 24,00 0,4835()(5,1 (Stilul modern 61,73 1,0

Stilul clasic 22,42 0,36

Stilul sport 42,22 0,68

VENIT

1.700.000 1.900.000 25,00 0,42

1.500.000 1.700.000 60,00 1,0

1.300.000 1.500.000 43,53 0,72

1.100.000 1.300.000 36,81 0,61

900.000 1.100.000 8,90 0,15

6,78$ ,(352)(6,21$/

Activitate pe cont propriu 57,35 0,95

$FWLYLWDWHVDODULDW 29,74 0,49Gospodine 27,42 0,45

RPHUL 31,15 0,526WXGHQ L 60,32 1,0Pensionari 31,07 0,51

MEDIU

Rural 28,07 0,58

Urban < 500.000 loc 25,00 0,51

Urban > 500.000 loc 48,62 1,0

4) 6HYD FDOFXODSHQWUX ILHFDUHJUXS GHYDULDELOHDPSOLWXGLQHDJUXSHLVXEIRUPDXQHLGLIHUHQ HvQWUHLFHDPDLPLF YDORDUHFDUHDUH]XOWDWvQXUPDFRPSDUD LHL

5) Se vor RUGRQDJUXSHOHGHYDULDELOHvQRUGLQHDGHVFUHVF WRDUHDDPSOLWXGLQLORU&HOHLPDLPDULDPSOLWXGLQLvLFRUHVSXQGHFHDPDLPDUHSXWHUHH[SOLFDWLY vQFHHDFHSULYHWHconsumul produsului.

QFRQVHFLQ YRPSXWHDRUGRQDDVWIHOFHOHYDULDELOH1. Venit2. Vrst3. 3UHIHULQ H4. 6LWXD LHSURIHVLRQDO 5. Mediu6. Sex)LHF UHL JUXSH , VH YD DWDD VHJPHQWXO FRQVLGHUDW UHSUH]HQWDWLY 9RP RE LQH DVWIHO DXGLHQ DUHSUH]HQWDWLY 1. Venit: 1.500.000 1.700.000


37/49

2. 9kUVW -44 ani3. 3UHIHULQ HVWLOXOPRGHUQ4. 6LWXD LHSURIHVLRQDO VWXGHQt5. Mediu: Urban (+ 500.000 loc)6. 6H[E UED L

2. 2 ILUP XWLOL]HD] GLIHULWH LQVWUXPHQWH SURPR LRQDOH vQ UHOD LLOH VDOH FX GLVWULEXLWRULL&RVWXOWRWDODOLQYHVWL LHLSURPR LRQDOHHVWHGHPLOXPUHSDUWL]DWGXS FXPXUPHD]

,QVWUXPHQWSURPR LRQDO InvHVWL LHXP

1. Publicitate 1.500.000

5HOD LLSXEOLFH 3.500.0003. Vizite organizate 765.000

'HPRQVWUD LL 575.0005. Mostre 85.000

6. Concursuri 2.575.000

TOTAL 9.000.000

$FHVWSURJUDPGHSURPRYDUHD IRVWSULPLWIRDUWHELQHGHF WUHLQWHrmediari. Astfel, au fostvQUHJLVWUDWHXQQXP UGHGHVROLFLW ULGLVWULEXLWHDVWIHO

,QVWUXPHQWSURPR LRQDO 6ROLFLW UL

1. Publicitate 4.450

5HOD LLSXEOLFH 10.8503. Vizite organizate 930


6. Concursuri 4.442

TOTAL 45.000

3ULQLQWHUPHGLXOFDPSDQLLORUSUHFHGHQWHILUPDDFRQVWDWDWF GLQQXP UXOWRWDOGHVROLFLW ULGRDUVHWUDQVIRUP vQYkQ] ULUHDOHFXRYDORDUHPHGLHGHXP

6 VHHYDOXH]H LQVWUXPHQWHOH SURPR LRQDOH XWLOL]DWH GLQ SXQFWGHYHGHUHDO UHQWDELOLW LLWLLQGF PDUMDGHSURILWHVWHGHGLQYkQ] UL

REZOLVARE:

Q SULPXO UkQG VH YRU HVWLPD YkQ] ULOH UHDOH SUHVXSXVH GH XWLOL]DUHD LQVWUXPHQWHORUSURPR LRQDOHSUH]HQWDWH3HQWUXDRE LQHDFHVWHYkQ] ULWUHEXLHGHWHUPLQDWQXP UXOGHRUGLQHGHYkQ]DUHSHQWUX ILHFDUHLQVWUXPHQW SURPR LRQDO vQ SDUWH 6-D HVWLPDWF GLQVROLFLW UL VH YRUtransforma n ordine de vnzare, astfel:

,QVWUXPHQWSURPR LRQDO 6ROLFLW UL Ordine de vnzare1. Publicitate 4.450 890,0

5HOD LLSXblice 10.850 2170,03. Vizite organizate 930 186,0

'HPRQVWUD LL 15.350 3070,05. Mostre 8.978 1795,6

6. Concursuri 4.442 888,4

TOTAL 45.000 9000,0


38/49

WLLQGF ILHFDUHRUGLQGH YkQ]DUHSUHVXSXQHvQPHGLHXP VH SRW HVWLPD YkQ] ULOHreale.

IQVWUXPHQWSURPR LRQDO 9kQ] ULXP


5HOD LLSXEOLFH 3.255.0003. Vizite organizate 279.000

'HPRQVWUD LL 4.605.0005. Mostre 2.693.400


TOTAL 13.500.000

3HQWUXDFDOFXODUHQWDELOLWDWHDILHF UXLLQVWUXPHQWSURPR LRQDOVHYDXWLOL]DXUP WRDUHDUHOD LH

rI =i

i

I

m, unde:

riUDWDUHQWDELOLW LLLQVWUXPHQWXOXLLmiPDUMDGHSURILWDVXSUDYkQ] ULORURE LQXWHSULQXWLOL]DUHDLQVWUXPHQWXOXLL

Ii = investi LDHIHFWXDW vQLQVWUXPHQWXOL3HQWUXDFDOFXOD UDWD UHQWDELOLW LLILHF UXLLQVWUXPHQW SURPR LRQDO PDLvQWkLVHYDFDOFXODPDUMDGHSURILWWLLQGF DFHDVWDUHSUH]LQW GLQYkQ] UL

Instrument

3URPR LRQDO9kQ] UL(u.m.)

Marja profitului 18%

(u.m.)

1. Publicitate 1.335.000 240.300

5HOD LLSXEOLFH 3.255.000 585.9003. Vizite organizate 279.000 50.220

'HPRQVWUD LL 4.605.000 828.9005. Mostre 2.693.400 484.812

6. Concursuri 1.332.600 239.868

TOTAL 13.500.000 2.430.000

Q IXQF LH GH DFHVWH YDORUL L GH YDORULOH LQYHVWL LLORU HIHFWXDWH VH YD SXWHD FDOFXOD DWkWUHQWDELOLWDWHD SHQWUX ILHFDUH LQVWUXPHQW SURPR LRQDO FkW L UHQWDELOLWDWHD PHGLH D FDPSDQLHLSURPR LRQDOH

,QVWUXPHQWSURPR LRQDO Rentabilitate

1. Publicitate 0,160

5HOD LL publice 0,167

3. Vizite organizate 0,066'HPRQVWUD LL 1,4425. Mostre 5,704

6. Concursuri 0,093

Rentabilitatea medie 0,270

'LQ FDOFXOHOH HIHFWXDWH UH]XOW F PRVWUHOH vQUHJLVWUHD] FHD PDL PDUH UHQWDELOLWDWH LDUrentabilitatea medie a campaQLHLSURPR LRQDOHHVWHGH


39/49


40/49

V = V1 + V2 SRWHQ LDOXOYkQ] ULORUWRWDOHGHE XWXULU FRULWRDUH6HYDRE LQHV = 860 mil. + 1000 mil. = 1860 mil. litri

VX = 186010080

80

+ = 826,66 mil. litri

VY = 186010080

100

+ = 1033,33 mil. litri

QORFXLQGUH]XOWDWHOHRE LQXWHvQUHOD LLOH L

2,Y2,X

2,X

1,Y1,X

1,X

LL

L1000

LL

L860

++

+= 826,66 mil. litri (9)

2,Y2,X

2,Y

,Y1,X

1,Y

LL

L1000

1LL

L860

++

+= 1033,33 mil. litri (10)

Obiectivul firmei X este acela de a-LPD[LPL]DYkQ] ULOHMax (Vx - Vy )

Vx - Vy = 2,y2,X

2,Y2,X

1,y1,X

1,Y1,X

LL

LL

1000LL

LL

860 +

++

(11)

&XUHVWULF LD/X,1 + LX,2Obiectivul firmei Y este similar celui al firmei X:

Max (VY VX )

VY VX =2,y2,X

2,X2,Y

1,y1,X

1,X1,Y

LL

LL1000

LL

LL860

+

++

&XUHVWULF LD/Y,1 +LY,2$FHVWHUHOD LLIRUPHD] GHIDSWPRGHOXOXQXLMRFFXVXP QXO vQFDUHYkQ] ULOHFkWLJDWHGH

X sunt pierdute de Y.

6ROX LDHVWHXUP WRDUHD

LX,i = V

V

L

iX

, i = 1,2

LY,i = LyV

Vi , i = 1,2

$WXQFLFkQGYkQ] ULOHILUPHLvQILHFDUHVHJPHQWVXQWSURSRU LRQDOHFXFKHOWXLHOLOHSXEOLFLWDUHHIHFWXDWHvQVHJPHQWXOUHVSHFWLYLDUYDULDQWDRSWLP VHRE LQH

Lx,1 =1860

86080 = 36,99 mil. u.m.

Lx,2 =1860

100080 = 43,01 mil. u.m.

Ly,1 =

1860

860100 = 46,24 mil. u.m.

Ly,1 =1860

1000100 = 53,76 mil. u.m.

9kQ] ULOHSHQWUXE XWXULOHGHWLSFRFD cola, pentru firma X:

VX,1 =24,4699,36

99,36860

+= 382,21 mil. litri

9kQ] ULOHSHQWUXE XWXULOHGHWLSFRFD cola, pentru firma Y;

VY,1 =24,4699,36

24,46860



41/49

9kQ] ULOHSHQWUXE XWXULU FRULWRDUHGHDOWWLS

VX,2 =76,5301,43

01,431000


VY,2 =76,5301,43

76,531000


4. ntr-R DQXPLW UHJLXQH SLD D XQXL SURGXV HVWH RFXSDW GH vQWUHSULQGHULOH $ L %vQWUHSULQGHULFDUHVHDGUHVHD] FXP UFLGLIHUHQ LDWHXQXLQXP UGHWUHLVHJPHQWHFDUHDOF WXLHVFSLD DUHVSHFWLY 9kQ] ULOHSRWHQ LDOHFDUHVXQWLQIOXHQ DWHGHSXEOLFLWDWHSHILHFDUHVHJPHQWVXQW

6HJPHQWXOPLOEXF L 6HJPHQWXOPLOEXF L 6HJPHQWXOPLOEXF L

%XJHWHOHSURPR LRQDOHDQXDOHDOHILUPHORU$L%VXQWGHPLOXPUHVSHFWLYPLOXPLILHFDUHILUP FXQRDWHEXJHWXOSURPR LRQDODOFHOHLODOWH

3UHVXSXQkQGF YkQ] ULOH ILHF UHL ILUPH vQFDGUXO ILHF UXL VHJPHQW VXQW SURSRU LRQDOH FXFKHOWXLHOLOHGHSXEOLFLWDWHHIHFWXDWH vQVHJPHQWXO UHVSHFWLYLF DPEHOHILUPHGRUHVFPD[LPL]DUHYkQ] ULORU WRWDOH V VH GHWHUPLQH GLVWULEX LD EXJHWHORU SURPR LRQDOH vQ VLWXD LD GH HFKLOLEUX LYkQ] ULOHILHF UHLILUPHvQDFHDVW VLWXD LH

REZOLVARE:

$DFXPUH]XOW GLQH[HPSOXODQWHULRUDWXQFLFkQGYkQ] ULOHILUPHLvQILHFDUHVHJPHQWVXQWSURSRU LRQDOHFXFKHOWXLHOile publicitare efectuate n segmentul respectiv punct de optim:

LA,i = LAV

Vi , i = 1,2,3

LBi = LBV

Vi , i =1,2,3

V = V1 + V2 + V3 = 300 + 800 + 600 =1700 mil. buc.

L A,1 = 1001700

300= 17,65 mil. u.m.

L A,2 = 1001700800 = 47,06 mil. u.m.

L A,3 = 1001700

600= 35,29 mil. u.m.

LB,1 = 901700

300= 15,88 mil. u.m.

LB,2 = 901700

800= 42,35 mil. u.m.

LB,3 = 901700

600= 31,76 mil. u.m.

9kQ] ULOHILUPHORU$L%YRUIL

VA,1 = 300 88,1565,17

65,17

+ = 157,92 mil. buc.

VA,2 = 80035,4206,47

06,47

+= 421,07 mil. buc.

VA,3 = 60076,3129,35

29,35

+= 315,79 mil. buc

VB,1 = 30065,1788,15

88,15

+= 142,08 mil. buc.


42/49


43/49

PC1999SUH XOGHYkQ]DUHPHGLXDOFRQFXUHQ HLvQDQXO99$SOLFkQGDFHDVW UHOD LHvQFD]XOILUPHLFRQVLGHUDWHVHRE LQH

P1994 = 1209.0 = 108 u.m.P1995 = 1200.1 = 120 u.m.P1996 = 1200.1 = 120 u.m.P1997 = 1209.0 = 108 u.m.P1998 = 1201.1 = 132 u.m.

&DQWLW LOHYkQGXWHVHSRWFDOFXODvQIXQF LHGHUHOD LDGLQWUHYkQ] ULOHILUPHLLFHOHDOHSLH HLFRWDGHSLD

qi = 1999MM

Eq

q

q , n care:

qiFDQWLWDWHDGHSURGXVHYkQGXW GHILUP vQDQXOL

M

E

q

qFRWDGHSLD DvQWUHSULQGHULL

qM1999YkQ] ULOHWRWDOHSHSLD vQ$VWIHOVHRE LQFDQWLW LOHYkQGXWHvQXOWLPLLDQLSHSLD

q1994 = 26002030

244 = 312 u.m.

q1995 = 26002180

306 = 364 u.m.

q1996 = 26002300

345= 390 u.m.

q1997 = 26002430

390= 416 u.m.

q1998 = 26002510

427= 442 u.m.

6LPLODUVHSURFHGHD] SHQWUXDGHWHUPLQDEXJHWHOHSURPR LRQDOH

Bi = 1999C

C

EB

B

B , n care:

Bi = bugetul promR LRQDOSHQWUXDQXOL

C

E

B

BUHOD LDGLQWUHEXJHWXOSURPR LRQDODOILUPHLEXJHWXOSURPR LRQDODOFRQFXUHQ HL

BC1999EXJHWXOSURPR LRQDODOFRQFXUHQ HLvQAstfel:

B1994 = 100003.0 = 3000 u.m.B1995 = 100002.0 = 2000 u.m.B1996 = 1000025.0 = 2500 u.m.B1997 = 100003.0 = 3000 u.m.B1998 = 100002.0 = 2000 u.m.

Vom calcula profiturile pentru perioadele considerate:

Pfo (1994) = ( )[ ]3000500031220108312 ++ = 19456 u.m.

Pfo

(1995) = ( )[ ]2000+5000+36420120364 = 29400 u.m.Pf

o(1996) = ( )[ ]2500+5000+39020120390 = 31500 u.m.

Pfo

(1997) = ( )[ ]3000+5000+41620108416 = 28608 u.m.Pf

o(1998) = ( )[ ]2000+5000+44220132442 = 42504 u.m.

9DORDUHDFHDPDLPDUHVHRE LQHvQDQXOFkQGVHYDIL[DXQEXJHWSURPR LRQDOGHGLQWRWDOXOEXJHWXOXLSURPR LRQDODOFRQFXUHQ HLGLQXPDGLF XP

3UH XOGHYkQ]DUHDOSURGXVHORUILUPHLYDILGLQSUH XOGHYkQ]DUHDOFRQFXUHQ HLp = 1,1 120 = 132 u.m.,


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iar valoarea profitului pentru anul 1999, va fi:

Pfo

(1999) = 42.504 u.m.

6. 2 ILUP DUH XQ EXJHW SURPR LRQDO GH PLO XP GLQ DFHVW EXJHW HVWH GHVWLQDWFKHOWXLHOLORUDIHUHQWHDQXQ XULORUvQUHYLVWHLHVWHGHVWLQDWFKHOWXLHOLORUDIHUHQWHDQXQ XULORUvQziare.

&LUFXOD LDLFRVWXODQXQ XULORUvQSULQFLSDOHOHUHYLVWHL]LDUHVXQWXUP WRDUHOH

InstrumentA

(36%)

&LUFXOD LH(u.m.)

Cost

(u.m.)

InstrumentB

(25%)

&LUFXOD LH(u.m.)

Cost

(u.m.)

Revista 1 3.024.503 285.000 Ziar 1 1.498.879 78.000

Revista 2 4.464.228 313.000 Ziar 2 971.957 85.000

Revista 3 2.157.978 187.000 Ziar 3 1.306.002 46.000

Revista 4 2.360.025 206.000 Ziar 4 1.101.615 63.500

Revista 5 849.688 108.000 Ziar 5 673.029 39.000

6 VHGHWHUPLQHQXP UXOWRWDOGHDQXQ XULLV VHVHOHF LRQH]HVXSRUWXULOHFHOHPDLDGHFYDWHWLLQGF ILUPDGRUHWHV XWLOL]H]HXQQXP UPD[LPGHDQXQ XULvQILHFDUHUHYLVW LDQXQ XULvQILHFDUH]LDUFXFRQGL LDXWLOL] ULLGRDUDVXSRUWXULORUDOF URUFRVWQXGHS HWHPHGLDSHILHFDUH

YDULDQW REZOLVARE:

%XJHWXO SURPR LRQDO DIHUHQW LQVWUXPHQWXOXL SXEOLFLWDU $ HVWH GH GLQ EXJHWXOSURPR LRQDO WRWDO LDU EXJHWXO DIHUHQW LQVWUXPHQWXOXL SXEOLFLWDU % HVWH GH GLQ EXJHWXOSURPR LRQDOWRWDO

n acest caz cheltuielile vor fi:Instrument A: 0,36 x 12.000.000 = 4.320.000 u.m.Instrument B: 0,25 x 12.000.000 = 3.000.000 u.m.

$FHVWHEXJHWHQXVXQWVXILFLHQWHSHQWUXDDFRSHULLFRVWXOWRWDOSHQWUXFHOHDQXQ XULvQWRDWHUHYLVWHOHLFHOHDQXQ XULvQWRDWH]LDUHOH&RVWXOWRWDOFHYDILOXDWvQFRQVLGHUDUHVHYDGHWHUPLQDvQIXQF LHGHQXP UXOGHDQXQ XULSHQWUXILHFDUHLQVWUXPHQWDVWIHO

Instrument A Cost unitar

(u.m.)

Cost total

(u.m.)

Revista 1 285.000 1.710.000

Revista 2 313.000 1.878.000

Revista 3 187.000 1.122.000

Revista 4 206.000 1.236.000

Revista 5 108.000 684.000

TOTAL - 6.594.000

Instrument B Cost unitar

(u.m.)

Cost total

(u.m.)

Ziar 1 78.000 780.000Ziar 2 85.000 850.000

Ziar 3 46.000 460.000

Ziar 4 63.500 635.000

Ziar 5 39.000 390.000

TOTAL - 3.115.000

$WkWFRVWXOWRWDOSHQWUXDQXQ XULOHGLQUHYLVWHFkWLFRVWXOWRWDOSHQWUXDQXQ XULOHGLQ]LDUHGHS HVFEXJHWHOHDIHUHQWHILHF UXLLQVWUXPHQW

QDFHVWFD]YDILQHFHVDUV VHVHOHF LRQH]HSHQWUXILHcare instrument suporturile cele maiFRQYHQDELOHDOF URUFRVWV QXGHS HDVF EXJHWXO


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3HQWUXDUHDOL]DDFHDVW VHOHF LHVHYDXWLOL]DFULWHULXOFDUHV SHUPLW RE LQHUHDXQHLDXGLHQ Hmaxime cu un cost minim.

n primul rnd se va calcula costulILHF UXLVXSRUWSHQWUXUHFHSWRULXWLOL]kQGIRUPXOD

Cmi = 1000A

C

i

ni , n care:

Cmi = costul suportului pentru fiecare 1000 receptoriCni = costul unitar al suportului i

AiDXGLHQ DVXSRUWXOXLLQXP UXOGHUHFHSWRUL

Instrument A Cost (Cmi)(u.m.)

Instrument B Cost (Cmi)(u.m.)

Revista 1 94,23 Ziar 1 52,04Revista 2 70,11 Ziar 2 87,45Revista 3 86,66 Ziar 3 35,22Revista 4 87,29 Ziar 4 57,64Revista 5 127,11 Ziar 5 57,95

6HOHF LDVHUHDOL]HD] XWLOL]kQGDFHOHVXSRUWXULFDUHQXGHS HVFFRVWXOPHGLXSHQWUX

UHFHSWRULvQFDGUXOILHF UXLLQVWUXPHQWQDFHVWHFRQGL LL

Cmi Cm

Cm =n

Cn

1

mi

Pentru reviste, costul mediu / 1000 este:Cm = 93,08 u.m.

Pentru ziare costul mediu / 1000 este:Cm = 58,06 u.m.

6XSRUWXULOHFRUHVSXQ] WRDUHILHF UXLLQVWUXPHQWQXGHS HVFYDORDUHDRE LQXW SHQWUXPHGLHsunt:

Instrument A: Revista 2 Instrument B: Ziar 1 Revista 3 Ziar 3 Revista 4 Ziar 4

Ziar 5

3HQWUX D GHPRQVWUD F FRVWXO WRWDO DO LQVWUXPHQWHORU DOHVH QX GHS HWH EXJHWXO SHQWUXILHFDUHLQVWUXPHQWVHYDFDOFXODVXPDWRWDO

Instrument A Cost unitar Cost total

Revista 2 313.000 1.878.000Revista 3 187.000 1.122.000Revista 4 206.000 1.236.000

TOTAL - 4.236.000


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Instrument B Cost unitar Cost total

Ziar 1 78.000 780.000

Ziar 3 46.000 460.000

Ziar 4 63.500 635.000

Ziar 5 39.000 390.000

TOTAL - 2.265.000

'LQFDOFXOHOHHIHFWXDWHUH]XOW F EXJHWXOGHVWLQDWLQVWUXPHQWXOXL$YDILXWLOL]DWDVWIHODQXQ XULvQUHYLVWHOHLLDUEXJHWXOGHVWLQDWLQVWUXPHQWXOXL%DQXQ XULvQ]LDUHOHXQWRWDOGHDQXQ XUL

7. 3URILWXULOHDQXDOH YLLWRDUHDOH XQHL ILUPH GHSLQG GHVWUDWHJLD SXEOLFLWDU XWLOL]DW L GHUHDF LD FRQFXUHQ HL 6WUDWHJLLOH DOWHUQDWLYH DOH ILrmei sunt: E1, E2, E3, E4 LDU FRQFXUHQ D SRDWHUHDF LRQDVXEIRUPD51, R2 sau R3 .

3URILWXULOHvQXQLW LPRQHWDUHSHFDUHILUPDOHYDRE LQHvQILHFDUHFD]vQSDUWHYRUIL

5HDF LLDOHFRQFXUHQ HLStrategiipublicitare R1 R2 R3

E1 150 300 450

E2 225 210 454,5

E3 240 165 525

E4 300 150 285

6 VHGHWHUPLQHVWUDWHJLDFHYDILXUPDW vQIXQF LHGHGLIHULWHFULWHULLGHFL]LRQDOHSHQWUXcriteriul HURWICZ se va lua n considerare un coeficient de optimism de 60%).

REZOLVARE:

a) Criteriul Laplace:

Strategii Profitul mediu

E1 (150 + 300 + 450) / 3 = 300

E2 (225 + 210 + 454,5) / 3 = 296,5

E3 (240 + 150 + 285) / 3 = 245

6WUDWHJLDDOHDV HVWH(3

b) Criteriul maximax sau optimist:

Strategii Profitul maxim

E1 450

E2 454,5

E3 525

E4 300

6WUDWHJLDDOHDV HVWH(3.


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c) Criteriul maximin sau pesimist:

Strategii Profitul minim

E1 150

E2 210

E3 165

E4 150

6WUDWHJLDDOHDV HVWH(2d) Criteriul Hurwicz ( = 0,6):

Strategii Maxim (Mi) Minim (mi) Hi = 0,6Mi + 0,4mi

E1 450 150 330

E2 454,5 210 356,7

E3 525 165 381

E4 300 150 270


e) Criteriul Savage. Matricea regretelor:

Strategii R1 R2 R3E1 150 0 75 150

E2 75 90 70,5 90

E3 60 135 0 135

E4 0 150 240 240


PROBLEME PROPUSE:

P1: 2 ILUP XWLOL]HD] GLIHULWH LQVWUXPHQWH SURPR LRQDOH vQ UHOD LLOH VDOH FX GLVWULEXLWRULL&RVWXOWRWDODOLQYHVWL LHLSURPR LRQDOHHVWHGHPLOXPUHSDUWL]DWGXS FXPXUPHD]

,QVWUXPHQWSURPR LRQDO ,QYHVWL LHXP


2. RHOD LLSXEOLFH 5.250.0003. Vizite organizate 1.500.000

'HPRQVWUD LL 1.125.0005. Mostre 375.000


TOTAL 15.000.000

$FHVW SURJUDP GH SURPRYDUH D IRVW SULPLW IRDUWH ELQH GH F WUH LQWHUPHGLDUL $VWIHO DX IRVWnregistrate uQQXP UGHGHVROLFLW ULGLVWULEXLWHDVWIHO

,QVWUXPHQWSURPR LRQDO 6ROLFLW UL

1. Publicitate 9.300

5HOD LLSXEOLFH 13.2503. Vizite organizate 1.100


6. Concursuri 6.400

TOTAL 50.000


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%XJHWHOHSURPR LRQDOHDQXDOHDOHILUPHORU$L%VXQWGHPLOXPUHVSHFWLYPLOXPLILHFDUHILUP FXQRDWHEXJHWXOSURPR LRQDODOFHOHLODOWH

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YkQ] ULORU WRWDOH V VH GHWHUPLQH GLVWULEX LD EXJHWHORU SURPR LRQDOH vQ VLWXD LD GH HFKLOLEUX LYkQ] ULOHILHF UHLILUPHvQDFHDVW VLWXD LH

Aplicatii Mk

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