Івченко І.Ю. Математичне програмування

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131

O 3.

+ 43

,!*,5  !



10 40 20 60 20

6 0

–Q 20

20 –Q

+Q 0

7 6 2

02675

07549

06372

–v

j 24570

50688

00007

01230





max '

= 2

–

min

= 20

L = 445

O 4.

+ 44

,!*,5  !



10 40 20 60 20

"

–Q 0

–Q 10

+Q 20

7 6 2

"

132

02675

07549

06372



–v

j 24370

50888

00207

01030







max '

= 1

–Q

min

= 0

L = 410

O 5.

+ 45

,!*,5  !



10 40 20 60 20

"

7 6 250 0

"

02675

07549

06372



–v

j 2336–1

50787

00106

10040





'  <= 0,   , L = 410.

133

  

1. %&!' ())  .

2. $ *   , ,  +?

3. :,'   .

4. $' '     *?

 

1. 

' '   .

 , :

1. : 20, 20, 40, 45 + 1338

: 8 6 2 6

7738

5245

:

25, 30, 40, 15

2. : 45, 35, 70 + 2534

: 6125

3438

: 20, 60, 55, 45

3. : 30, 70, 50 + 2736

: 9457

5762

: 10, 40, 20, 60

4. : 40

, 30, 50 + 1725

: 3841

6 3 5 3

: 40, 20, 60

5. : 30, 40, 70, 60 + 1972

: 3155

6834

2313

: 35, 80, 25, 70

6. : 50, 20, 35 + 1338

: 8626

4773

: 25, 30, 40, 15

134

7. : 30, 40, 70 + 1972

: 3155

6834

: 35, 40, 25, 70

8. : 30, 5, 45, 70 + 37154

: 75863

64832

31742

: 30, 35, 25, 25, 35

9. : 130, 90, 80 + 456810

: 1032315

4105116

: 110, 30, 50, 30, 90

10. : 60, 55, 40, 35 + 1297

: 3465

6483

4331

: 70, 5, 45,

11. : 20, 16, 14, 11 + 2397

: 3461

5122

4581

: 16, 18, 12, 15

12. : 68, 55, 40 + 18 2 9 7

: 304155

6483

: 42, 25, 33, 56

13. : 130, 90, 100, 140 + 2368

: 8123

7441

2851

: 110, 50, 90, 60

14. : 60, 40, 100, 50 + 8 12 4 9 10

: 751536

946127

53264

: 30, 80, 65, 35,

135

15. : 50, 40, 20 + 3241

: 2315

3274

: 30, 25, 35, 20

16. : 40, 25, 35 + 10 5 7 4

: 74910

61487

: 15, 40, 30, 15

17. : 60, 65, 70 + 2432

: 3123

5415

: 40, 60, 70, 25

18. : 40, 30, 20 + 1264

: 3132

5751

: 30, 25, 15, 20

19. : 60, 70, 20 + 2451

: 2394

3425

: 40, 30, 30, 50

20. : 50, 20, 30, 20 + 1334

: 5275

6482

7157

: 40, 30, 35, 15

 

K  (  %++)

,    :

1. -, ;

2. ) ;

3. ' .

136

 13

83  (9 4: 

1. 

383 43 3

@   < ,  <

! 

¦¦

, (13.1)

*  ’   " >-

 ,      !, $

¦¦

ba (13.2)

$

¦¦



ba (13.3)

%   (13.2)   "  -

>   $

, $

1



¦¦

def

bba

. (13.4)

*  , # $=  $  -

>

ax d

(13.5)

*   (13.3)

1



¦¦

aab (13.6)

bx d

. (13.7)

@       " -

  p-$   (13.5)

1,1,21,1

,...,,

 qpqq

xxx ,  

1, 





¦¦¦¦

bxax , (13.8)

137

*   

qpp

,11,1

,...,



,  

1,1 

 

¦¦¦¦¦¦

pij

aabxbx (13.9)

?  =     -

     <    -

 $>   (2- ) $

= (1- ).

*    $    !-

 = 0.

2. E

(8 5

K $! $   $=,  

     $ >. A , #

   $ $’ . $ -

   ! " " $"

(< >  M   $ < " 

 #   ’).

O =   $  >,  -

" $= < , $  

ijij

dx d ,



constd

.

* ’ <     

= , #  $,   0t

-

 

ijij

d . *    =  

’   = $  -

 . * #   ,   =

! ’.

3. 

 3 8

F  m  $ $! p  <

 $’!,

a , mi ,1 , pk ,1 , ($’! < -   i-

 $).

A  !  n  = 

$’!,

b , pknj ,1,,1 .

138

'  

ijk

—  > 

-  <  i-  j- =.

F

ijk

— $’!  -   i-  j-.

F,

¦¦

k = 1, p

mino

¦¦¦

ijkijk

ijk

, ,,1 mi pk ,1

ikijk

bx ,,1 nj pk ,1

ijk

x .,,, kji

A   .

J#  #   , #   = $

  ,   4- 

.

$"   $ = ’

<    ( ). C-

$"  -. *   m, n, p,

…,    $"! 

<< ’ ! -

=.

  

1. $  ' ,   ?

2. K;  ,  .

3. K; ,    ;

 !   .

4. $     ?

139

 14

F4  (

1. 

 3 F4 3

O <  :; !  .

=   :;    = -

    "  :;, # ! -

<>  <. %  >! ,

    $ ’ = $>   

. )   :; 

<< < ! -

 ’ = <     -

  .

C  :;    .

'!  , #    .

max o L (x)=

i 1

(14.1)

 :

i 1

= b

(i = 1, m) (14.2)

j 0 (14.3)

*$   

L (X) = (C, X)c (14.1c)

AX = B (14.2c)

X = j0

(14.3c)

@<> >   (14.7)—(14.9) $ :

 , #   < 

L (y) =

i 1

o min. (14.4)

 

i 1

> = c

(j = 1, n), x

> = 0. (14.5)

*$   

L (Y) = (B, X)c (14.10c)

140

; YA > = B. (14.11c)

' ) $   . , # !

 (14.4)—(14.5), %. ., ,   ! 

min L     ,  ’  -

’!,  > :;, >  ’ -

 .

?  (14.4)—(14.5)     :; (14.1)—

(14.3):

1. ' $=

(14.1)—(14.3) !  

(14.4)—(14.5);

2. '  (14.1)—(14.3) !  $=

(14.5);

3.    (14.4)—(14.5) ! > -

>   (14.1)—(14.3);

4.  (14.4)—(14.5) —  min L,  (14.1)—(14.3) —

m L;

5. $=  "  $= ;

6.   $<  n  m.

 (14.1)—(14.3) ! <,  (14.4)—(14.5) —

<>  <.

2. 

 (  3 E. 3

&  :;   $= .

  X = (x

…, x

), #  max <  L:

L (x) = (C, X) =

i 1

N max (14.6)

 

i 1

<= b

(i=1, m) (14.7)

> = 0

(14.8)

@  #$  , <  (14.6)—(14.8),

> !    . A $ 

>   (# $>)  x

n + i

(i = 1, m).

j 1

+ x

n+i

= b

; i = n,1 (14.7`)

j 0; j = mn ,1 (14.8`)