, .. n=2, , .. , . . .
: Z=C1x1+C2x2 (1)
(2)
x1 ³ 0, x2 ³ 0. (3)
, (2) (3) , .. , . (2) (3), , : ai1x1+ai2x2=bi (i=1,2,...,m), x1=0, x2=0. ( ) .
.
, , .. C1x1+C2x2 = const. . - N=(C1,C2).
, .
: , C1x1+C2x2 = const Z .
(2) Z=0 (. .). Z=C1x1+C2x2 N=(C1,C2), C1x1+C2x2=0 N.
. , ( A C), Z A, - C. C(x1,x2) , BC CD.
, .
1. C1x1+C2x2 = const, N , . , .
2. , , . (a), (), ().
.
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1. .
2. , .
3. , N=(C1,C2) , .
4. , .
5. , , , .
6. , , . , . .
7. .
, .
) . Z = 2x1 + 3x2 , x1 ³ 0, x2 ³ 0.
. (. ). x10x2
, x1 = 0, x2 = 0.
OABCDE.
2x1 + 3x2 = 0 - N=(2; 3) O , . Z = 0 N. . , C, Z . C CD.
.
: x1=6; x2=4. x1 x2 , Lmax = 2×6+3×4=24.
, , 24 , 6 . P1 4 . P2.
b) .
L = 4x1 + 6x2 x1³0, x2³0.
. (.). x10x2
, x1 = 0, x2 = 0.
, . A, B, C,D.
, N=(4; 6) 4x1 + 6x2 = 0 (L). L N. . , B; N, , , B . B L1 L2; .
: x1=2; x2=3. , Lmin = 4×2+6×3=26.
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, (26 . ), 2 I 3 II.