4.
max Z = x12+x22
x1x2 £ 4
x1 + x2 ³ 5
x1 £ 7
x2 £ 6
x1³ 0, x2 ³ 0
: D KLMN (.4).
Z = 1, x12+x22 =1 - (0;0) , 1. Z = 4, - (0;0) , 2. Z, , D KLMN. . .
Z.
; (; 6).
Z.
; .
. 4. : D KLMN. , max Z = .
ABCD C(2/3;6), KLMN - (7;4/7). , .
Z , , max Z = . .
1. f() , , , .
2. f() () , , , .
1. ?
2. ?
3. ?
4. ?
5. ?
6. ?
[1]
1. f(x), f(x) f() (. . 5).
2. f(x), f(x) f() (. . 5).
. .
, y=f(x) , , f() = 0 .
, , .. , ( ). , . , - , . , , , . () .
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. . y=f(x) , y=f(x), , - .
. . f ¢(x) ,
. 5.
f ²() , f(x); f ²(x) , - .
y=f(x) .
1. y¢=f(x).
2. , f¢(x)=0 .
3. .
4. ( ) .
y=f(x) , ( 1,2,4). 3, : f ²(x) .
5. p , (a < p, λ > 0). .
. x. px .
1.
2. : ( ).
3.
( ), , C(x) .
4. (.. )
.
, , . , , . .
, , . . x=0 . x=0 , . , . , , .
6. 350 . . , . .
. x. 350x .
1.
2. : ( ).
3.
( ), , , .. = 1,354007 C(x) .
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4. (.. )
.
1,354007, 198, 59 . .
, , .
.
y(t) , t. , p, .. . t Y(t)=py(t). I(t) , . , () , . y¢(t)= l I(t) (1)
( , .. , ).
, I(t) ,
I(t)=mY(t)=mpy(t) (2),
m ( ) , 0<m<1.
I(t)=mY(t)=mpy(t) y¢(t)=lI(t),
y¢=ky, (3), k=mpl.
. , .. p y p=p(y) ( ).
y¢=mlp(y)y (4).
, y¢>0, y(t). y(t) . , y¢=mlp(y)y ,
y²=mly¢ .
( ) . y y²=mly¢p .
, , y(t) ; , , y(t) .
p(y)=a+by, (4) y¢=mlp(y)y, m- , l-
(5)
(5) .
(6)
(6), ,
(6) , .
Ay + aB + Bby = 1
(A + Bb)*y + aB = 1 <=>
(7)
(5)
(-)
(8)
, = (9)
(10).
(10) .
, .. (0), (9) .
7. y=y(t), , p(y) p(y)=2-y, l=2, m=0,5, y(0)= 0,5.
.
y ¢=mlp(y)y
y=(2-y)y
,
,
. 6.
, y(0)=0,5, , C=3. y , . .6.
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