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3.4. ÷ÁÒÉÁÎÔÙ ËÏÎÔÒÏÌØÎÏÊ ÒÁÂÏÔÙ ½6 107
4.
x
1
− x
2
6 1,
2x
1
+ x
2
> 2,
x
1
− 2x
2
> 0,
x
1
> 0, x
2
> 0,
f = x
1
+ 3x
2
→ max .
5.
2x
1
+ 3x
2
> 6,
x
1
− 2x
2
> −9,
5x
1
− 3x
2
6 15,
x
1
> 0, x
2
> 0,
f = −4x
1
+ 3x
2
→ max .
6.
2x
1
− x
2
6 6,
x
1
− 3x
2
> −6,
x
1
+ 2x
2
6 −6,
x
1
> 0, x
2
> 0,
f = x
1
+ 3x
2
→ max .
7.
x
1
+ 2x
2
6 14,
5x
1
− 3x
2
> −15,
x
1
− 3x
2
6 −3,
x
1
> 0, x
2
> 0,
f = x
1
+ x
2
→ max .
8.
x
1
+ 2x
2
6 12,
x
1
− x
2
6 4,
2x
1
− 3x
2
6 4,
x
1
> 0, x
2
> 0,
f = 2x
1
+ 3x
2
→ max .
9.
2x
1
+ x
2
6 10,
2x
1
− 3x
2
> −6,
x
1
+ 2x
2
> 4,
x
1
> 0, x
2
> 0,
f = 2x
1
+ 8x
2
→ max .
úÁÄÁÎÉÅ 5.
îÁÊÔÉ ÜËÓÔÒÅÍÁÌÉ ÓÌÅÄÕÀÝÉÈ ÆÕÎËÃÉÏÎÁÌÏ×.
0. J[y(x)] =
ln 2
R
0
((y
0
)
2
+ 3y
2
)e
2x
dx, y(0) = 0, y(ln 2) = 1;
1. J[y(x)] =
1
R
0
(y
02
+ 9y
2
− 3x) dx, y(0) = 0, y(1) = 1;
3.4. ÷ÁÒÉÁÎÔÙ ËÏÎÔÒÏÌØÎÏÊ ÒÁÂÏÔÙ ½6 107
x − x2 6 1,
1
2x1 + x2 > 2,
4.
x1 − 2x2 > 0,
x > 0, x > 0,
1 2
f = x1 + 3x2 → max .
2x + 3x2 > 6,
1
x1 − 2x2 > −9,
5.
5x1 − 3x2 6 15,
x > 0, x > 0,
1 2
f = −4x1 + 3x2 → max .
2x − x2 6 6,
1
x1 − 3x2 > −6,
6.
x1 + 2x2 6 −6,
x1 > 0, x2 > 0,
f = x1 + 3x2 → max .
x + 2x2 6 14,
1
5x1 − 3x2 > −15,
7.
x1 − 3x2 6 −3,
x1 > 0, x2 > 0,
f = x1 + x2 → max .
x + 2x2 6 12,
1
x1 − x2 6 4,
8.
2x1 − 3x2 6 4,
x1 > 0, x2 > 0,
f = 2x1 + 3x2 → max .
2x + x2 6 10,
1
2x1 − 3x2 > −6,
9.
x1 + 2x2 > 4,
x1 > 0, x2 > 0,
f = 2x1 + 8x2 → max .
úÁÄÁÎÉÅ 5.
îÁÊÔÉ ÜËÓÔÒÅÍÁÌÉ ÓÌÅÄÕÀÝÉÈ ÆÕÎËÃÉÏÎÁÌÏ×.
ln
R2 0 2
0. J[y(x)] = ((y ) + 3y 2 )e2x dx, y(0) = 0, y(ln 2) = 1;
0
R1
1. J[y(x)] = (y 02 + 9y 2 − 3x) dx, y(0) = 0, y(1) = 1;
0
