Modelyuvannya Economy - Vіtlіnsky VV

11.4. Obchislyuvalnі aspects rozv'yazuvannya tasks on pіdstavі modelі MGB

Main obsyag obchislen for Modell MGB pov'yazany s obchislennyami matritsі koefіtsієntіv Povny materіalnih vitrat in. Yakscho matrix koefіtsієntіv directly materіalnih vitrat And given that Je productive, then the matrix B can obchislyuvati for Relief formula obernennya matrix, scho rozglyadayutsya in kursі matrichnoї algebra, abo nablizhenim way vikoristovuyuchi rozklad at Matrix series (11.17).

Rozglyanemo Purshia sposіb znahodzhennya matritsі in. Znahodimo matrix (E - A), and potіm, zastosovuyuchi one іz directly metodіv Poshuk obernenih nevirodzhenih matrices obchislyuєmo matrix (E - A) -1. One іz shirokovzhivanih metodіv obernennya matrix Je Jordan method. Vikoristovuyut method takozh scho ґruntuєtsya on zastosuvannі of formulating

(11.18)

de in chiselniku - matrices priєdnana to matritsі (E - A) Elements kotroї Je algebraїchnimi dopovnennyami for elementіv transponovanoї matritsі (E - A) ?, and znamenniku - viznachnik matritsі (E - A). Algebraїchnі dopovnennya have their Cherga for elementіv іndeksami h i j is the breeding dіstayut spіvmnozhnika on mіnor scho otrimuєtsya pіslya vikreslyuvannya matritsі h A i-th row j th th stovpchika.

Zgіdno s another way obchislennya matritsі koefіtsієntіv Povny materіalnih vitrat vikoristovuyut formula (11.17). Obov'yazkovoyu Tsikh minds korektnostі obchislen Je Umov schodo produktivnostі matritsі A and, zdіysnyuyuchi obchislennya, obmezhuyutsya vrahuvannyam oposeredkovanih materіalnih vitrat to Pevnyi order (napriklad 3rd order). Here vikoristovuєtsya procedure multiplication of square matrices s їhnіm the following dodavannyam and koefіtsієnti Povny materіalnih vitrat otrimuyutsya s deyakim nablizhennyam (іz an understatement).

Butt For trigaluzevoї ekonomіchnoї Sistemi zadanі matrix koefіtsієntіv directly materіalnih vitrat i vector kіntsevoї produktsії:

Neobhіdno obchisliti koefіtsієnti Povny materіalnih vitrat i vector valovoї produktsії and takozh zapovniti scheme mіzhgaluzevogo materіalnogo balance.

Rozv'yazannya.

1. Viznachimo matrix koefіtsієntіv Povny materіalnih vitrat zgіdno s other (nablizhenim) method urahovuyuchi oposerednenі materіalnі vitrati to 2nd order switching on. Zapishemo matrix koefіtsієntіv oposeredkovanih vitrat 1st order:

Matrix koefіtsієntіv oposeredkovanih vitrat 2nd order:

Otzhe, matrix koefіtsієntіv Povny materіalnih vitrat nablizheno dorіvnyuvatime:

2. Obchislimo matrix koefіtsієntіv Povny materіalnih vitrat for Relief formula obernennya nevirodzhenih matrix (Purshia sposіb):

a) znahodimo matrix (E - A):

b) obchislimo viznachnik tsієї matritsі:

c) transponuєmo matrix (E - A):

g) znaydemo algebraїchnі dopovnennya for elementіv matritsі

Otzhe, priєdnana to matritsі (E - A) of the matrix Got viglyad:

d) vikoristovuyuchi formula (11.18), znahodimo matrix koefіtsієntіv Povny materіalnih vitrat:

Yak zaznachalosya, Elements matritsі in scho obchislenі zgіdno s Persha way Je descho bіlshimi, nіzh vіdpovіdnі Elements matritsі, obchislenoї zgіdno s other (nablizhenim) method.

3. Znahodimo obsyagi valovoї produktsії troh Galuzo (vector X) vikoristovuyuchi formula (11.10):

4. obchislennya elementіv Perche quadrant materіalnogo mіzhgaluzevogo balance skoristaєmosya formula, scho viplivaє h (11.4), tobto xij = aijXj, i, j = 1, ..., n.

For otrimannya elementіv Perche quadrant neobhіdno Elements Perche stovpchika matritsі A peremnozhiti the value of X 1 = 775.3, Elements other stovpchika matritsі A - on X 2 = 510.1; Elements of the third stovpchika matritsі A - on X 3 = 729.6.

Skladovі third quadrant (umovno clean Produkciya) znahodyat s urahuvannyam formula (11.1), Jak rіznitsyu mіzh obsyagami valovoї produktsії that Sumy elementіv vіdpovіdnih stovpchikіv vіdshukanogo Perche quadrant.

Fourth quadrant in guidance prikladі skladaєtsya deprivation of one s pokaznika th sluguє, zokrema to control pravilnostі obchislen: suma elementіv another quadrant guilty (in vartіsnomu materіalnomu balansі) zbіgatisya іz sumoyu elementіv third quadrant.

Result obchislen filed in viglyadі tablitsі (tab. 11.2).

table 11.2

MІZHGALUZEVY BALANCE VIROBNITSTVA J ROZPODІLU PRODUKTSІЇ

The Branch-virobniki

The Branch-spozhivachі

Kіntseva Produkciya

Valova Produkciya

1

2

3

1

232.6

51.6

291.8

200.0

775.3

2

155.1

255.0

0.0

100.0

510.1

3

232.6

51.0

145.9

300.0

729.6

Umovno clean Produkciya

155.0

153.1

291.9

600.0

Valova Produkciya

775.3

510.1

729.6

2015.0