NỘI DUNG THẢO LUẬN TOÁN

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  B1;=>? @ 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 !"#$%&'(&)*+( &)&Đ ́ ươ III.   #                    #?   DE%F& ( ) 1,2,0,0,0x = '&(#?<G,'& ( ) 2 3 4 5 1 2 3 5 1 2 4 5 1 2 3 4 2 2 2 max 2 3 4 4 5 3 6 2 2 3 0, 1,5 j f x x x x x x x x x x x x x x x x x x j = + - - ® ì ï - + + + = ï ï ï - + - = - ï ï í - + + - = ï ï ï ï ³ = ï ï î 3 )&&<$+-)& . 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  #  $>JKL73M 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)      { } .46=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 36 = − + + + → + − − + ≤ −   + + − =   − − + − ≥ −   ≥ =  j f x x x x x x x x x x x x x x x x x x x x j     %:   ( ) 7767=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.37.777MVL>JMKR4    !  !  " # $  1.            D%FGWX'&# 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    AY  :            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      $"       Z       0    :    H0T# Z       %9    ?    0 Z %                       Z I      $         A  