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1. Thế nào là phương án cực biên, điều kiện cần và đủ để một phương án là phương án cực biên?
!"#$ ( ) 1 2 1 2 2 1 2 1 2 2 max 2 2 1 0 2 1 4 3 f x x x x x x x x x x = + đ ỡ ù - Ê - ù ù ù Ê ù ù ớ ù + Ê - ù ù ù - + Ê ù ù ợ %&&#&''&( ( ) ( ) 1 2 3 4 2 1 7 1 1,0 , , , 7, 1 , , 3 6 9 9 x x x x ổ ử ổ ử ữ ữ ỗ ỗ ữ ữ = - = - - = - - = - - ỗ ỗ ữ ữ ỗ ỗ ữ ữ ỗ ỗ ố ứ ố ứ 2. )&*$+,)&-)& . /01)&*2&'&# a) ( ) 3 . 4 5 3 4 6 5 . 4 6 5 3 6 3 . . 3 6 5 6 7 5 = + + = + + = + + = = j f x x x x x x x x x x x x x x x x j b) 8 9 !" %: # ( ) = + + đ ỡ ù + + = ù ù ù - + = ớ ù ù = ù ù ợ 1 2 3 1 2 3 1 2 3 1) 3 2 max 1 1 0, 1,2,3 j f x x x x x x x x x x x j ( ) 1 2 3 1 2 3 1 2 3 1 2 3 2) min 1 1 1 f x x x x x x x x x x x x x = + + đ ỡ ù - + + Ê ù ù ù - - - Ê ớ ù ù - - + Ê ù ù ợ 3 )&*$+-)&&(;)& 3. <'';=>?@%9 ? A B1;=>? @ 4 /01)&*2&'&# ( ) 3 . 4 6 3 . 4 6 3 . 4 6 3 . 4 6 3 5 6 4 4 3 6 C . . 4 6 5 7 6 j f x x x x x x Min x x x x x x x x x x x x x x j = + - + + ® ì - + - + = ï ï ï ï - + - = ï ï í - + - = ï ï ï ï ³ = ï ï î Đ ́ ( ) 3 . 3 . 3 . 3 . . 3 4 3 3 . 3 . 4 . 7 f x x x x Max x x x x x x x x x x = + - ® ì + - £ ï ï ï ï + + £ - ï ï í ï + - £ ï ï ï ³ ï ï î !"#$%&'(&)*+( &)&Đ ́ ươ III. # #? DE%F& ( ) 1,2,0,0,0x = '&(#?<G,'& ( ) 2 3 4 5 1 2 3 5 1 2 4 5 1 2 3 4 2 2 2 max 2 3 4 4 5 3 6 2 2 3 0, 1,5 j f x x x x x x x x x x x x x x x x x x j = + - - ® ì ï - + + + = ï ï ï - + - = - ï ï í - + + - = ï ï ï ï ³ = ï ï î 3 )&&<$+-)& . H#&3)&$'&< 4 /01)&&<2&'&# a) ( ) 3 . 3 . 3 . 3 . 4 6 3 5 3 . 3 7 7 . j f x x x x Min x x x x x x x x x x j = + - ® ì + + £ ï ï ï ï + - = ï ï í + - = ï ï ï ï ³ = ï ï î I # $>JKL73M b) ( ) 3 . 3 . 3 . 3 . 3 3 4 3 3 4 4 7 . j f x x x x Min x x x x x x x x x x j = + - ® ì - + = ï ï ï ï - + = ï ï í + - ³ ï ï ï ï ³ = ï ï î I # $N 1. N A O: A 2. )&9 A$+-)& . a) 9 A #?P : 9 A #?% O A ( ) 3 . 3 . 4 3 . 6 3 . 5 . 3 4 6 Q R 3 4 3 3 . 3 3 7 5 = + + → − + + = − + − + = − − + + = ≥ = j f x x x x x x x x x x x x x x x x x j b) { } .46=J # A #?: 9 A ( ) 3 3 . 4 3 4 3 4 6 3 3 . . 3 7 6 = + → − + + = − − + = − + + = ≥ ∀ = j f x x x x x x x x x x x x x x j 1. ? A? 9 A ? ? 9 0 3 " 3. " >? %9 ? A : >? 4. P # ( ) 3 . 3 . 3 . 3 . 3 3 3 3 6 3 3 7 . = − − → + − ≤ − + ≤ + ≤ − ≤ ≥ ∀ = j f x x x x x x x x x x x x x x x j %9 ?? 9 A A ? ? ? 9 A 9 0 3 ( ) 3 . 4 6 3 . 4 6 . 4 6 3 . 6 6 C 6 Q . 3 5 3 3 4 R 3 4 37 7 36 = − + + + → + − − + ≤ − + + − = − − + − ≥ − ≥ = j f x x x x x x x x x x x x x x x x x x x x j %: ( ) 7767=x A 9 A . 9 A #?P : 9 A #?% O A ( ) 3 . 3 . 3 3 . 4 Q . 3 4 3 4 3 3 . 7 . = + + → − + − ≤ + ≥ − + ≤ − ≥ = j f x x x x x x x x x x x x x j ! ! " # $ 8 9 !" %: # ( ) = - ® ì ï + £ ï ï ï + £ ï ï í ï + ³ ï ï ï ³ ³ ï ï î 1 2 1 2 1 2 1 2 1 2 1) 3 min 2 5 10 2 6 2 2 0, 0 f x x x x x x x x x x x ( ) = + + ® ì ï + + ³ ï ï ï - - = ï ï ï ï - - £ í ï ï + £ ï ï ï ï + ³ ï ï î 1 2 3 1 2 3 1 2 3 1 2 3 1 3 2 3 2) 3 7 min 6 3 2 14 4 5 12 4 10 2 7 f x x x x x x x x x x x x x x x x x 3 >? %9 ? : >? 9 0 . ST A 9 # 0 4 P !"#? ( ) 3 . 4 6 3 4 6 3 . 4 6 3 6 3 6 4 6 5 3 C .3 3 U 3 . U 6 .7 . .5 7 6 j f x x x x x x Min x x x x x x x x x x x j = + + + - ® ì - - - = ï ï ï ï + + + = ï ï í + £ ï ï ï ï ³ = ï ï î I # $>JKL.37.777MVL>JMKR4 ! ! " # $ 1. D%FGWX'&# x '&G $ ( ) ( ) = + ® ì ï - + + + = ï ï ï - + + + = ï ï í ï + = ï ï ï ³ ï ï î = - 2 4 1 2 3 4 1 2 3 4 2 4 1 ) min 2 1 2 2 3 2 3 0 0, 1,0,3 a f x x x x x x x x x x x x x x x ( ) ( ) = + ® ì ï + + + = ï ï ï + + + £ ï ï í ï - + + + = ï ï ï ³ ï ï î = - 1 4 1 2 3 4 1 2 3 4 1 2 3 4 1 ) max 1 3 2 4 9 4 16 0 0,1,3, 3 b f x x x x x x x x x x x x x x x x x 3 %9 ? 9 T A 9 ? 9 0 % 0? # : 9 . %9 ? !": 9 : 9 AY : A 4 P !"#: 9 A ( ) 3 . 4 6 3 . 4 6 3 . 4 6 3 . 4 6 3 5 6 4 4 3 6 C . . 4 6 5 7 6 j f x x x x x x Min x x x x x x x x x x x x x x j = + - + + ® ì - + - + = ï ï ï ï - + - = ï ï í - + - = ï ï ï ï ³ = ï ï î Yêu cầu: Z : 0 Z [A $" Z 0 : H0T# Z %9 ? 0 Z % Z I $ A