I BA C -5 5 13 0 0 0 b X1 X2 X3 X4 X5 X6 -------------------------------------------------------------- 1 X2 5 20 -1 1 3 1 0 0 2 X5 0 10 16 0 -2 -4 1 0 3 X6 0 -10 5 0 (-4) -3 0 1 -------------------------------------------------------------- Cj-Zj -100 0 0 -2 -5 0 0 采用对偶单纯形迭代，x6出基，x3进基， -------------------------------------------------------------- I BA C -5 5 13 0 0 0 b X1 X2 X3 X4 X5 X6 -------------------------------------------------------------- 1 X2 5 25/2 11/4 1 0 -5/4 0 3/4 2 X5 0 15 27/2 0 0 -5/2 1 -1/2 3 X3 13 5/2 -5/4 0 1 3/4 0 -1/4 -------------------------------------------------------------- Cj-Zj -95 -5/2 0 0 -7/2 0 -1/2 最优解 MAX Z= 95
变量名 取值 检验数 X1 0 -2.500000 X2 25/2 X3 5/2
X4 0 -3.500000 X5 15
X6 0 -0.500000
约束标号 对偶价格 ( 1) 3.500000 ( 2) 0.000000 ( 3) 0.500000
在最优基不变的条件下, 变量在目标函数中的系数的取值区间 变量名 现系数 系数取值区间
X1 -5.0000 ( - ? , -2.5000 ) X2 5.0000 ( 4.3333 , 7.8000 ) X3 13.0000 ( 8.3333 , 15.0000 ) X4 0.0000 ( - ? , 3.5000 ) X5 0.0000 ( -0.1852 , 1.0000 ) X6 0.0000 ( - ? , 0.5000 )
在最优基不变的条件下, 右端常数项的取值区间
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约束序号 现常数 常数取值区间
( 1) ( 2) ( 3) 20.0000 90.0000 50.0000 ( ( ( 16.6667 , 75.0000 , 33.3333 , 26.0000 60.0000 ? ) ) )
12．设 max Z?2x1?5x2?8x3 ??3x1?2x2?x3?610 s.t.???x1?6x2?3x3?125? ??x?x112?
?2x3?420??x1,x2,x3?0（1）求在不影响最优基的条件下各个cj的允许变化的范围。 （2）求在不影响最优基的条件下各个bi的允许变化的范围。 解：列单纯形表求解得最优表，利用最优基不变时求解各系数区间MAX: 2X1 +5X2 +8X3 ST: 1]
3X1 +2X2 -1X3 +1X4 2] MAX: 2X1 +5X2 +8X3 3] -1X1 -1X1 +6X2 +1X2+1/2X3 +3X3 +1X5 =610 =125 ST: +1X6 =420 1] 2]
-1X1 3X1 +6X2 +2X2 +3X3 -1X3 +1X4 +1X5 =610 得到了第一个可行基3] -1X1 +1X2+1/2X3 +1X6 =420 =125 用最大检验数法
--------------------------------------------------------- I BA -----------------------------------------------------------
C b X1 2 X2 5 X3 8 X4 0 X5 0 X6 0
1 2 X4 X5 0 610 0 125 -1 3 6 2 -1 3 1 0 0 1 0 -----------------------------------------------------------
3 X6 0 420 -1 1 1/2 0 0 1 0 125/3 840 ----------------------------------------------------------- Cj-Zj 0 2 5 8 0 0 0 旋转元是 A[2][3] 用最大检验数法
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------------------------------------------------------------------- I BA C 2 5 8 0 0 0
b X1 X2 X3 X4 X5 X6 -------------------------------------------------------------------
1 X4 0 1955/3 8/3 4 0 1 1/3 0 1955/8 2 X3 8 125/3 -1/3 2 1 0 1/3 0 3 X6 0 2395/6 -5/6 0 0 0 -1/6 1 --------------------------------------------------------------------
Cj-Zj -1000/3 14/3 -11 0 0 -8/3 0 -------------------------------------------------------------------- 旋转元是 A[1][1] 用最大检验数法
------------------------------------------------------------------- I BA C 2 5 8 0 0 0 b X1 X2 X3 X4 X5 X6 ------------------------------------------------------------------- 1 X1 2 1955/8 1 3/2 0 3/8 1/8 0 2 X3 8 985/8 0 5/2 1 1/8 3/8 0 3 X6 0 9645/16 0 5/4 0 5/16 -1/16 1 -------------------------------------------------------------------- Cj-Zj -5895/4 0 -18 0 -7/4 -13/4 0 -------------------------------------------------------------------- 迭代次数 = 2 最优解
MAX Z= 5895/4 = 1473 3/4 = 1473.750000
变量名 取值 检验数 X1 1955/8 = 244 3/8 = 244.375000
X2 0 -18.000000 X3 985/8 = 123 1/8 = 123.125000
X4 0 -1.750000 X5 0 -3.250000 X6 9645/16 = 602 13/16 = 602.812500
约束标号 对偶价格 ( 1) 1.750000 ( 2) 3.250000 ( 3) 0.000000
(1) 在不影响最优基的条件下各个cj的允许变化的范围 ?j?cj?CBB?1Pj?0在最优基不变的条件下, 变量在目标函数中的系数的取值区间 变量名 现系数 系数取值区间
X1 2.0000 ( -2.6667 , ? ) X2 5.0000 ( - ? , 23.0000 ) X3 8.0000 ( 0.8000 , ? )
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X4 0.0000 ( - ? , 1.7500 ) X5 0.0000 ( - ? , 3.2500 ) X6 0.0000 ( -5.6000 , 52.0000 ) （2）在不影响最优基的条件下各个bi的允许变化的范围Bb’≥0 在最优基不变的条件下, 右端常数项的取值区间 约束序号 现常数 常数取值区间
( 1) 610.0000 ( -41.6667 , ? ) ( 2) 125.0000 ( -203.3333 , 9770.0000 ) ( 3) 420.0000 ( -182.8125 , ? )
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