Введение в специальность / 14 - Vv_v_sp_11 - zad mnotr sv

! "#

$ n %"

%"

&'

" ( # ) *&+ " "$ + ,-

$ ". , # " (

!"

! & % $

, /

"# & 0 !"

! + 1($ $ , /

" ($

" " " 2

/

! / "# ") 3+ " + ,-

4 ". , # " (

%" + 2

, ("

," / "# "

% 5 + / ' , / + "

6) 7 2

1$ 1 + !

8

# +

." ( & $%

," "#

%" ," +

, +

, &' %" " )

* , "

( , 49

(

! & :

xi ; + ,-

$ i2# " (

%" " "

" +

, <

xij

; + "

+ ,-

i2# " ( 4 j2# " (

%" . + , <

bi

; ! + , i2# " ( 0 & 1 + !

"$ 8

#

+

5 ( !

& xi 0 xij 0 bi

%$4$ 0 " + " ( 0 " "( &' ,

-"'6)

= ' ,$

% + "

%","!

0 1 "

&+ (

$ . " ( &'

$% #

+ " " + ,-

4 +

, " "

n

xi ≥ X xij + bi, i =

1, n.

j=1

$ 0 !

>" &

+

% , "

". , #

" (

1 %/ "

!2

& ) + % , &' > " 0

$($49

'$ + ,-

# , /

'

" ( # ," / "# "0 ". ,"$ " ( + 1($

, /

> " &

5 & "

"(& 0 ( /

4 0 , & & 0 $ "1 &

1 , "

$

), )6) ?". ,

%

' > " . 1& / "

! 0

$%

! + % , & 9

". , # i2# " ( / " ! &

# (

!

# di ) @ " (

! "0 !

, 0 " "

di

= min dsi,

s

/, dsi

; + , ( , + &+ " + ,-

i2#

" 2

( 4 +

! ( 8 / "

! / s2/ >" ") 7" 1 "% 0 + ( !

/ "

! $ :

0 ≤ xi ≤ di, i =

1, n.

ci

; 1 + % , " ,

-& + ,-

i2# "2

( ) 7 /," %" " &

! / "# " " &

n

% " )

P cixi

' 1' ,

i=1

* ( ! " xij

= aij '" "

% ( ! + ,-

i2# " (

0

xj

, 9 " +

% , ,

-& + ,-

j2# " (

) ( 2

" $($ $ , " !

- #

# 0 * ) + ,( 2

. ( ,($ ". , / " " " / +

," ( !

& aij 1 " % " ! "

aij ,

j =

1, n

"%& "4

+ ,&, 9 / +

,") "

- A =

i = 1, n

)

3 ! / &8 "%" / + ( !" ( , 49 4 , ( %","!

. " ( &' $% # ! / "# ":

n

X cixi → min,

5 ) 6

i=1

n

xi − X aij xj ≥ bi, i =

1, n.

5 ) 6

j=1

0 ≤ xi ≤ di, i =

1, n,

5 ) 6

(

2 " ! # >

c 0x → min,

(E − A)x ≥ b,

0 ≤ x ≤ d.

","!

+ , 1 / +" "%& "4

)

= ( , "

$ # %","!

+ "%"(

0 ! (

1 %","!"

8 $ 0

(

1 8 %" ( ! ci 0 i =

1, n

)

,+ ( . 0 ! &+ ($4$ (

$

n

X aij < 1, i =

1, n,

j=1

& ( , &' &8 1 % "!

#

"( & " "

n

X xij < xj , j =

1, n

5 ) 6

j=1

5

' " "' (

! & & "."4$ " "(

% 2

0 "

6)

" " 5 ) 6 (

$' #! #

0 " + "

( 0 &2

+ ($4$ )

! # !

%

$ % "!"4 0 ! %" " & 2

," j2# " (

, (. & + &8 " %" " & ," , /

' " ( # " + 2

,-

4 0 + " ($4 j2# " ( )

)! )" , &

# )$)$( 8 # + "%" 0 ! +

&+ (

( 2

# 5 ) 6 8

x0 & "

#

(E − A)x = b

5 )%6

A&