【正文】 0 10/3 0 此時(shí)對偶問題的解為 Y ＝（ 0， 10/3， 0， 2/3， 0 ）代入 Minw=5y1+2y2+4y3 . 3y1+ y2+2y3y4=4 6y1+3y2+5y3y5=10 yi≥0(i=1,2,…,5) 不是對偶問題的可行解 44 對原問題進(jìn)行迭代得： cj 4 10 0 0 0 CB XB b x1 x2 x3 x4 x5 θ 4 x1 1 1 0 1 2 0 10 x2 1/3 0 1 1/3 1 0 0 x5 1/3 0 0 1/3 1 1 cjzj 0 0 2/3 2 0 此時(shí)對偶問題的解為 Y＝（ 2/3， 2， 0， 0， 0）代入 Minw=5y1+2y2+4y3 . 3y1+ y2+2y3y4=4 6y1+3y2+5y3y5=10 yi≥0(i=1,2,…,5) 是對偶問題的可行解 45 單純形法求解的過程，從對偶的觀點(diǎn)來看，是在始終保持原始可行解的條件下，不斷改進(jìn)對偶可行性的過程。 63 Maxz=3x14x2 . x1+2x2≥2 3x1+ x2≥4 x1 x2≤1 x1+ x2≤3 x1,x2≥0 Maxz=3x14x2 . x12x2≤2 3x1 x2≤4 x1 x2≤1 x1+ x2≤3 x1,x2≥0 Maxz=3x14x2 . x12x2+x3=2 3x1 x2+x4=4 x1 x2+x5=1 x1+ x2+x6=3 xj≥0 64 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 0 x3 2 1 2 1 0 0 0 0 x4 4 3 1 0 1 0 0 0 x5 1 1 1 0 0 1 0 0 x6 3 1 1 0 0 0 1 cjzj 3 4 0 0 0 0 可以看出，這時(shí)候原問題和對偶問題都不可行 列出初始單純形表： 65 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 0 x3 2 1 2 1 0 0 0 0 x4 4 3 1 0 1 0 0 0 x5 1 1 1 0 0 1 0 0 x6 3 1 1 0 0 0 1 cjzj 3 4 0 0 0 0 66 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 0 x3 2 1 2 1 0 0 0 0 x4 4 3 1 0 1 0 0 － 4 0 x5 1 1 1 0 0 1 0 0 x6 3 1 1 0 0 0 1 cjzj 3 4 0 0 0 0 67 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 0 x3 2 1 2 1 0 0 0 0 x4 4 3 1 0 1 0 0 － 4 0 x5 1 1 1 0 0 1 0 0 x6 3 1 1 0 0 0 1 cjzj 3 4 0 0 0 0 4 x2 4 3 1 0 1 0 0 68 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 0 x3 2 1 2 1 0 0 0 0 x4 4 3 1 0 1 0 0 － 4 0 x5 1 1 1 0 0 1 0 0 x6 3 1 1 0 0 0 1 cjzj 3 4 0 0 0 0 0 x3 6 5 0 1 2 0 0 4 x2 4 3 1 0 1 0 0 69 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 0 x3 2 1 2 1 0 0 0 0 x4 4 3 1 0 1 0 0 － 4 0 x5 1 1 1 0 0 1 0 0 x6 3 1 1 0 0 0 1 cjzj 3 4 0 0 0 0 0 x3 6 5 0 1 2 0 0 4 x2 4 3 1 0 1 0 0 0 x5 5 4 0 0 1 1 0 70 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 0 x3 2 1 2 1 0 0 0 0 x4 4 3 1 0 1 0 0 － 4 0 x5 1 1 1 0 0 1 0 0 x6 3 1 1 0 0 0 1 cjzj 3 4 0 0 0 0 0 x3 6 5 0 1 2 0 0 4 x2 4 3 1 0 1 0 0 0 x5 5 4 0 0 1 1 0 0 x6 1 2 0 0 1 0 1 71 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 0 x3 2 1 2 1 0 0 0 0 x4 4 3 1 0 1 0 0 － 4 0 x5 1 1 1 0 0 1 0 0 x6 3 1 1 0 0 0 1 cjzj 3 4 0 0 0 0 0 x3 6 5 0 1 2 0 0 4 x2 4 3 1 0 1 0 0 0 x5 5 4 0 0 1 1 0 0 x6 1 2 0 0 1 0 1 cjzj 15 0 0 4 0 0 72 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 0 x3 2 1 2 1 0 0 0 0 x4 4 3 1 0 1 0 0 － 4 0 x5 1 1 1 0 0 1 0 0 x6 3 1 1 0 0 0 1 cjzj 3 4 0 0 0 0 0 x3 6 5 0 1 2 0 0 6/5 4 x2 4 3 1 0 1 0 0 4/3 0 x5 5 4 0 0 1 1 0 5/4 0 x6 1 2 0 0 1 0 1 cjzj 15 0 0 4 0 0 73 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 0 x3 6 5 0 1 2 0 0 6/5 4 x2 4 3 1 0 1 0 0 4/3 0 x5 5 4 0 0 1 1 0 5/4 0 x6 1 2 0 0 1 0 1 cjzj 15 0 0 4 0 0 3 x1 6/5 1 0 1/5 2/5 0 0 74 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 0 x3 6 5 0 1 2 0 0 6/5 4 x2 4 3 1 0 1 0 0 4/3 0 x5 5 4 0 0 1 1 0 5/4 0 x6 1 2 0 0 1 0 1 cjzj 15 0 0 4 0 0 3 x1 6/5 1 0 1/5 2/5 0 0 4 x2 2/5 0 1 3/5 1/5 0 0 75 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 0 x3 6 5 0 1 2 0 0 6/5 4 x2 4 3 1 0 1 0 0 4/3 0 x5 5 4 0 0 1 1 0 5/4 0 x6 1 2 0 0 1 0 1 cjzj 15 0 0 4 0 0 3 x1 6/5 1 0 1/5 2/5 0 0 4 x2 2/5 0 1 3/5 1/5 0 0 0 x5 1/5 0 0 4/5 3/5 1 0 76 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 0 x3 6 5 0 1 2 0 0 6/5 4 x2 4 3 1 0 1 0 0 4/3 0 x5 5 4 0 0 1 1 0 5/4 0 x6 1 2 0 0 1 0 1 cjzj 15 0 0 4 0 0 3 x1 6/5 1 0 1/5 2/5 0 0 4 x2 2/5 0 1 3/5 1/5 0 0 0 x5 1/5 0 0 4/5 3/5 1 0 0 x6 7/5 0 0 2/5 1/5 0 1 77 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 0 x3 6 5 0 1 2 0 0 6/5 4 x2 4 3 1 0 1 0 0 4/3 0 x5 5 4 0 0 1 1 0 5/4 0 x6 1 2 0 0 1 0 1 cjzj 15 0 0 4 0 0 3 x1 6/5 1 0 1/5 2/5 0 0 4 x2 2/5 0 1 3/5 1/5 0 0 0 x5 1/5 0 0 4/5 3/5 1 0 0 x6 7/5 0 0 2/5 1/5 0 1 cjzj 0 0 3 2 0 0 78 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 0 x3 6 5 0 1 2 0 0 6/5 4 x2 4 3 1 0 1 0 0 4/3 0 x5 5 4 0 0 1 1 0 5/4 0 x6 1 2 0 0 1 0 1 cjzj 15 0 0 4 0 0 3 x1 6/5 1 0 1/5 2/5 0 0 4 x2 2/5 0 1 3/5 1/5 0 0 2 0 x5 1/5 0 0 4/5 3/5 1 0 1/3 0 x6 7/5 0 0 2/5 1/5 0 1 7 cjzj 0 0 3 2 0 0 79 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 3 x1 6/5 1 0 1/5 2/5 0 0 4 x2 2/5 0 1 3/5 1/5 0 0 2 0 x5 1/5 0 0 4/5 3/5 1 0 1/3 0 x6 7/5 0 0 2/5 1/5 0 1 7 cjzj 0 0 3 2 0 0 0 x4 1/3 0 0 4/3 1 5/3 0 80 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 3 x1 6/5 1 0 1/5 2/5 0 0 4 x2 2/5 0 1 3/5 1/5 0 0 2 0 x5 1/5 0 0 4/5 3/5 1 0 1/3 0 x6 7/5 0 0 2/5 1/5 0 1 7 cjzj 0 0 3 2 0 0 3 x1 4/3 1 0 1/3 0 2/3 0 0 x4 1/3 0 0 4/3 1 5/3 0 81 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 3 x1 6/5 1 0 1/5 2/5 0 0 4 x2 2/5 0 1 3/5 1/5 0 0 2 0 x5 1/5 0 0 4/5 3/5 1 0 1/3 0 x6 7/5 0 0 2/5 1/5 0 1 7 cjzj 0 0 3 2 0 0 3 x1 4/3 1 0 1/3 0 2/3 0 4 x2 1/3 0 1 1/3 0 1/3 0 0 x4 1/3 0 0 4/3 1 5/3 0 82 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 3 x1 6/5 1 0 1/5 2/5 0 0 4 x2 2/5 0 1 3/5 1/5 0 0 2 0 x5 1/5 0 0 4/5 3/5 1 0 1/3 0 x6 7/5 0 0 2/5 1/5 0 1 7 cjzj 0 0 3 2 0 0 3 x1 4/3 1 0 1/3 0 2/3 0 4 x2 1/3 0 1 1/3 0 1/3 0 0 x4 1/3 0 0 4/3 1 5/3 0 0 x6 4/3 0 0 2/15 1/5 1/3 1 83 cj 3 4 0 0 0 0 CB XB b x1 x2 x3 x4 x5 x6 θ 3 x1 6/5 1 0 1/5 2/5 0 0 4 x2 2/5 0 1 3/5 1/5 0 0 2 0 x5 1/5 0 0 4/5 3/5 1 0 1/3 0 x6 7/5 0 0 2/5 1/5 0 1 7 cjzj 0 0 3 2 0 0 3 x1 4/3 1 0 1/3 0 2/3 0 4 x2 1/3 0 1 1/3 0 1/3 0 0 x4 1/3 0 0