Оформлення КП

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1. 1.1. .....5 1.2. ....5 1.3. ....6 1.4. 11 1.4.1. 11 1.4.2. .12 1.4.3. ...14 1.4.4. ..15 1.5. ...16 1.5.1. 16 1.5.2. 18 1.5.3. () 21 2. 2.1. 24 2.1.1. Microsoft Excel..24 2.1.2. Minimize Maximize MathCAD........25 2.1.3 Minimize Maximize Maple...27 2.2. Excel, MathCad, Maple29 51 ... .. .. .. .. ,

2 50

. . . .

2.3. .31 2.4. .36 2.5. Microsoft Excel, MathCAD, Maple38 2.6. ......41

3

, , , , . , . , , . , , . , , . . - Exel, MathCAD Maple, , . , , , , , , . , , . . - Exel, MathCAD Maple. 4

. , .

5

1 1.1. , , . , , 220 260 . . (. 1.1): 1.1 1 2 , . 1 4 50 , . ., F 1 1 3 1 5 1 2 4 1 3 30 35 30 35 40

G 1 3 35

, 65% , 3:2, F G 3:4. , . 1.2. , , . 6

, , , , . , . . 1.3.

, . (), . : () , , , ,

. () . , .

: ) ; ) . , : ) ; 7

) ; ) . . : ) ; ) . , . ( ) , , . : ) ; ) . . . : ) ; ) . , . : ) ; : ) ; 8

.

:

1.4. , . , , , , , . . , , , . 1.4.1. . , (, , , , , F, G), (1 2). , 65% , 3:2, F G 3:4. , . 1.1 . x , 1 x2 ,x3 ,

x4 , 9

x5 ,x6 F,

x7 G. , , : F ( x) = 50 x1 + 30 x 2 + 35 x3 + 30 x 4 + 35 x5 + 40 x6 + 35 x7 max : x1 + x 2 + x3 + 3 x 4 + x5 + 5 x6 + x7 220 4 x1 + x 2 + 2 x3 + 4 x 4 + x5 + 3x6 + 3x7 260 2 x1 3x 2 = 0 4 x 6 3 x7 = 0 x 2 = ( x1 + x 2 + x3 + x 4 + x5 + x6 + x7) * 0.651, 2, x3, x 4, x5, x 6, x 7 0

1.4.2. . : 1) . , (, ). ( , ). (. 1.2):

10

1.2 , . ., 1 2 , .. 1 4 1 1 1 2 3 4 1 1 F 5 3 G 1 3

220 260

6 8

50

30

35

30

35

40

35

0,4

0,3

0,6

0,5

0,8

0,9

0,6

, , , . :

{ ( 50;0.4) x1 + ( 30;0.3) x 2 + ( 35;0.6) x3 + ( 30;0.5) x 4 + ( 35;0.8) x5 + ( 40;0.9) x6 + ( 35;0.6) x7 } max P{ x1 + x 2 + x3 + 3x 4 + x5 + 5 x6 + x 7 ( 220;6) } 0.9 P { 2 x1 3x 2 ( 0;0.6 )} 0.6 P { 4 x6 3x7 ( 0;0.4)} 0.7 P{ 4 x1 + x 2 + 2 x3 + 4 x 4 + x5 + 3x6 + 3 x7 ( 260;8)} 0.7

P { 0.35 x 2 0.35 x1 0.35 x3 0.35 x 4 0.35 x5 0.35 x6 0.35 x7 = ( 0;0.6 )} 0.8

1, 2, x3, x 4, x5, x 6, x 7 0

2) 1.4.1 , . , ( ) , .

11

i ( ) i . , , 0,6; 0,4; 0,7; 0,3; 0,7; 0,8; 0,7. , 0.7 0.8. (. 1.3). 1.3. , . .,

i1 2 , .. 1 4

i0,7 0,6

i1 1

i0,4 0,6

i1 2

i0,9 0,7

i3 4

i0,8 0,9

i1 1

i0,5 0,6

F

i5 3

i0,7 0,8

G

i1 3

i0,6 0,8 220 260

50

0,6

30

0,4

35

0,7

30 0.3

35

0,7

40

0,8

35

0,7

: P{ N ( 50;0.6) x1 + N ( 30;0.4) x 2 + N ( 35;0.7 ) x3 + N ( 30;0.3) x 4 + N ( 35;0.7 ) x5 + N ( 40;0.8) x6 + N ( 35;0.7 ) x 7 } max

P{ N (1;0.7) x1 + N (1;0.4) x 2 + N (1;0.9) x3 + N (3;0.8) x 4 + N (1;0.5) x5 + N (5;0.7) x6 + N (1;0.6) x7 220} 0.8 P{ N (4;0.6) x1 + N (1;0.6) x 2 + N (2;0.7) x3 + N (4;0.9) x 4 + N (1;0.6) x5 + N (3;0.8) x6 + N (3;0.8) x7 260} 0.6 P { N (2;0.2) x1 N (3;0.4) x2 0} 0.6 P { N (4;0.7) x6 N (3;0.6) x7 0} 0.7 P {N (0.35;0.02) x 2 N (0.35;0.03) x1 N (0.35;0.04) x3 N (0.35;0.02) x 4 N (0.35;0.02) x5 N (0.35;0.01) x6 N (0.35;0.04) x7 = 0} 0.8

1, 2, x3, x 4, x5, x 6, x 7 0

13

1.4.3. 1.4.1, , , , , .

( u1

1),...,uk ) , ui - , i - (

u i . , , 48 .. 0,2, 50 .. 0,9 51 .. 0,3. :

{( 48;0.2, (50;0,9),(51;0,3)}x1 + {(29;0.4), ( 30;0.8) , (32;0.3)}x2 + {(32;0.2),( 35;0.8) , (36;0.3)}x3 + ) + {(34;0.4),( 35;0.8) , (38;0.6)}x7 m ax

+ {(28;0.6),( 30;0.7 ) , (32;0.4)}x 4 + {(33;0.2),( 35;0.9) , (37;0.6)}x5 + {(37;0.2),( 40;0.8) , (42;0.3)}x6 +

{(0.8;0.3), (1;0.9), (1.2;0.4)}x1 + {(0.6;0.2), (1;0.7), (1.4;0.6)}x 2 + {(0.6;0.2), (1;0.9), (1.4;0.7)}x3 + + {(2.5;0.4), (3;0.8), (3.4;0.6)3}x 4 + {(0.7;0.6), (1;0.9), (1,7;0.2)}x5 + + {(4;0.6), (5;0.8), (7;0.2)}x6 + {(0.6;0.2), (1;0.8), (1.3;0.4)}x7 {( 200;0.4) , (220;0.8), (250;0.6)} {(3;0.4), (4;0.8), (5;0.6)}x1 + {(0.9;0.7), (1;0.9), (1.3;0.4)}x 2 + {(1.5;0.6), (2;0.7), (2.6;0.8)}x3 + + {(3.6;0.3), (4;0.9), (4.7;0.8)}x 4 + {(0.8;0.4), (1;0.8), (1.3;0.6)}x5 + {(2;0.6), (3;0.7), (4;0.6)}x6 + + {(2;0.7), (3;0.9), (5;0.6)}x7 {( 240;0.3) , (260;0.7), (270;0.2} { (1;0.3), (2;0.8), (3;0.6)}x1 {(2;0.6), (3;0.9), (4;0.7)}x2 = {( 0.3;0.1), ( 0;0.9) , (0.6;0.4)} { (3;0.6), (4;0.8), (5;0.4)}x6 {(2;0.7), (3;0.9), (4;0.6)}x7 = {( 0.4;0.2) , (0;0.8), (0.7;0.6)} {(0.3;0.2), (0.35;0.7), (0.4;0.3)}x 2 {(0.31;0.3), (0.35;0.8), (0.39;0.6)}x1 {(0.32;0.4), (0.35;0.8), (0.41;0.1)}x3 {(0.33;0.6), (0.35;0.7), (0.36;0.1)}x 4 {(0.34;0.3), (0.35;0.9), (0.37;0.7)}x5 {(0.3;0.4), (0.35;0.8), (0.4;0.1)}x6 {(0.32;0.4), (0.35;0.7), (0.36;0.6)}x7 = {( 0.4;0.2) , (0;0.8), (0.4;0.3} 1, 2, x3, x 4, x5, x 6, x 7 0

14

1.4.4. , . , . . 1. F1. 2. F2. : F1( x) = 50 x1 + 30 x 2 + 35 x3 + 30 x 4 + 35 x5 + 40 x6 + 35 x7 max F 2( x) = (0.02 * 50) x1 + (0.04 * 30) x 2 + (0.05 * 35) x3 + (0.01* 30) x 4 + (0.02 * 35) x5 + + (0.01* 40) x6 + (0.02 * 35) x7 min F1: x1 + x 2 + x3 + 3 x 4 + x5 + 5 x6 + x7 220 4 x1 + x 2 + 2 x3 + 4 x 4 + x5 + 3x6 + 3x7 260 2 x1 3x 2 = 0 4 x 6 3 x7 = 0 x 2 = ( x1 + x 2 + x3 + x 4 + x5 + x6 + x7) * 0.651, 2, x3, x 4, x5, x 6, x 7 0

F2: x1 + x 2 + x3 + 3 x 4 + x5 + 5 x6 + x7 220 4 x1 + x 2 + 2 x3 + 4 x 4 + x5 + 3x6 + 3x7 260 2 x1 3x 2 = 0 4 x 6 3 x7 = 0 x 2 = ( x1 + x 2 + x3 + x 4 + x5 + x6 + x7) * 0.6550 x1 + 30 x 2 + 35 x3 + 30 x 4 + 35 x5 + 40 x 6 + 35 x7 F1 1, 2, x3, x 4, x5, x 6, x 7 0

15

1.5. . :n

c xi =1 j n

j

max(min) :

(1.1)

a xj =1 ij

j

bj___

x j 0, j = 1, n

(1.2)

(Exel, MathCAD, Maple). . : 1. . : ci (mi ; i ) bi (mi ; i ) : M { c j ( )} maxj =1 n

(1.3)

(1.4)

: P{ aij ( ) b j } ij =1 n

(1.5) (1.6)

0 i 1

16

. :n

c xi =1 j n

j

max(min)

(1.7)

:

a xj =1 ij

j

bj___

~

x j 0, j = 1, n

(1.8)

bi (m, ) . : bi = m 2.~ 1

(1 i )

(1.9)

. . : ci (mi ; i ) aij (mi ; i ) : M { c j ( )} maxj =1 n

(1.10)

(1.11)

:

M {aij }x j + kij =1

n

D{a }xj =1 ij

n

2 j

bj (1.12) 17

x j 0, j = 1, n

___

ki

(ki ) = 1 i

. c j , b j , aij .

:

{(cj =1

n

j

| c j ( x1 )),...,(c j | c j ( xn ))}x j max____

(1.13)

xi = 1,3 . :n

{(aj =1

ij

| aij ( x1 )),...,( aij | aij ( xn ))}x j {(bi | bi ( x1 )),...,(bi | b i ( xn ))}___

x j 0, j = 1, n

(1.14)

, . : ~ A = ( u1 A ( u1 ) ) ,..., ( u k A ( u k ) ) 1) k

a=

ui A (ui )i =1

i =1 . ~ 2) A = ( A ( u1 ) u1 ),..., ( A ( u k ) u k )

A (ui )

k

a=

j A ( ui ) i =1

j

min

1k A ( ui ) 2 i =1

(u )j

.

~ A = ( A ( u1 ) u1 ),..., ( A ( u k ) u k ) 3)

a= :

u i G

uiG , G

, ~ A , G G . 4) : a = max ( G ) , G , ~ A . , , . 5) G , ~ A . , : , . 1.6. a = min ( G ) ,

. , n : F1 F2 ... Fn . ( ) . 1. F1 = 1 F2 = 2 ... Fn = n . i = 1 . . i * Fi . i

i . i = n , , 19

* n . i = i .

, i = i + 1 i . , , , . : 0. . , , , F1 F2 . 1. , , . : F1( x) = 50 x1 + 30 x 2 + 35 x3 + 30 x 4 + 35 x5 + 40 x6 + 35 x7 max F1: x1 + x 2 + x3 + 3 x 4 + x5 + 5 x6 + x7 220 4 x1 + x 2 + 2 x3 + 4 x 4 + x5 + 3x6 + 3x7 260 2 x1 3x 2 = 0 4 x 6 3 x7 = 0 x 2 = ( x1 + x 2 + x3 + x 4 + x5 + x6 + x7) * 0.65

1, 2, x3, x 4, x5, x6, x7 0 : ,x112,00

,28,00

,30,00

,40,00

,5200,00

F,60,00

G,70,00

7840. 2. :

50 x1 + 30 x 2 + 35 x3 + 30 x 4 + 35 x5 + 40 x6 + 35 x 7 F1 , , , , . 20

: F 2( x) = (0.02 * 50) x1 + (0.04 * 30) x 2 + (0.05 * 35) x3 + (0.01* 30) x 4 + (0.02 * 35) x5 + + (0.01* 40) x6 + (0.02 * 35) x7 min

21

F2: x1 + x 2 + x3 + 3 x 4 + x5 + 5 x6 + x7 220 4 x1 + x 2 + 2 x3 + 4 x 4 + x5 + 3x6 +