将aA1x1+a42x2+…+axn=b写为两个等价的不等式 akr, +akx ≥b akx+ak2x2+…+aonx≤b 或 x ≤b x b 代入(Ⅰ)式得出线性规划 x,+c2l a1x1+a12x2+…+a1nxn≤b a21x1+a2x2+…+a2nxn≤b2 akx, +ak2x ≤b (I) +,+a_x.≤b x1, x.≥0 得对偶关系表如表2-4 表2-4 x a12 a a 由对偶关系表得出(Ⅰ)的对偶规划 G=bW+bW2+…+bW-bW” b w w,+a,n wr-akw Wm≥C1 a12W+a22+…+a2Wk Wn≥C2 …+a +aW≥C. W,Wk",…,Wm≥0将ak1 x1 + ak 2 x2 +"+ akn xn = bk 写为两个等价的不等式：    + + + ≤ + + + ≥ k k kn n k k k kn n k a x a x a x b a x a x a x b " " 1 1 2 2 1 1 2 2 或    − − + − ≤ − + + + ≤ k k kn n k k k kn n k a x a x a x b a x a x a x b " " 1 1 2 2 1 1 2 2 代入（Ⅰ）式得出线性规划 1 1 2 2 11 1 12 2 1 1 21 1 22 2 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 2 max , , , 0 n n n n n n k k kn n k k k kn n m m mn n n Z C x C x C x a x a x a x b a x a x a x b a x a x a x b s t a x a x a x b a x a x a x b x x x = + + +  + + + ≤  + + + ≤    + + + ≤ ⋅  − − − − ≤ −    + + + ≤   ≥ " … … ……………………………… " " ……………………………… … … k m (Ⅱ) 得对偶关系表如表 2-4 表 2-4 x1 x2 … xm … xn c1 c2 … cm … cn W1 a11 a12 … a1m … a1n b1 W2 a21 a22 … a2m … a2n b2 ┇ ┇ ┇ ┇ ┇ ┇ ┇ ┇ Wk ' ak1 ak2 … akm … akn bk Wk '' -ak1 -ak2 … -akm … -akn -bk ┇ ┇ ┇ ┇ ┇ ┇ ┇ ┇ Wm am1 am2 … amm … amn bm 由对偶关系表得出（Ⅰ）的对偶规划 1 1 2 2 11 1 21 2 1 1 1 1 12 1 22 2 2 2 2 2 1 1 2 2 1 2 min , , , , , , 0 k k k k k k k m m k k k m m k k k m m n n kn k kn mn m k k m G bW b W b W b W b W a W a W a W a W a W C a W a W a W a W a W C s t a W a W a W a W a W C W W W W W n = + + + ′ − ′′+ +  + + + ′ ′ − ′+ + ≥  + + + ′ ′ − ′+ + ≥ ⋅  + + + ′ ′ − ′+ + ≥ ′ ′′ ≥ " " " " " " """""""""""""""""" " " " "       ∧ maxZ minG ∧ ∧ ∧ ≤ ≤ ≤ ≤ ≤