案例.投资策略设三种投资基金的数量分配分别为x1,x2,x3,其单位为1000000(百万)。投资方案为一下:目标函数:maxz=0.18x1+0.125x2+0.075x3<1>约束方程为:X1+x2+x3<=0.8X1>=0.16X1<=0.32X2>=0.16X2<=0.4X3>=0.240.125x1+0.0875x2+0.0125x3=0.05X1,x2,x3>=0**********************最优解如下*************************目标函数最优值为:.094145变量最优解相差值-----------------------x1.2490x2.160x3.3910约束松弛/剩余变量对偶价格----------------------------10.0632.07103.08904.24050-.026.151070.933目标函数系数范围:变量下限当前值上限-------------------------------x1.15.18.75x2无下限.125.145x3.018.075无上限常数项数范围:约束下限当前值上限-------------------------------1.664.81.62.249.32无上限3无下限.16.2494.16.4无上限5.053.16.2936无下限.24.3917.04.05.058<2>目标函数:maxz=0.18x1+0.125x2+0.075x3约束方程为:X1+x2+x3<=0.8X1>=0.16X1<=0.32X2>=0.16X2<=0.4X3>=0.240.125x1+0.0875x2+0.0125x3=0.055X1,x2,x3>=0**********************最优解如下*************************目标函数最优值为:.098765变量最优解相差值-----------------------x1.2930x2.160x3.3470约束松弛/剩余变量对偶价格----------------------------10.0632.02703.13304.24050-.026.107070.933目标函数系数范围:变量下限当前值上限-------------------------------x1.15.18.75x2无下限.125.145x3.018.075无上限常数项数范围:约束下限当前值上限-------------------------------1.704.822.293.32无上限3无下限.16.2934.16.4无上限5.12.16.366无下限.24.3477.04.055.058<3>目标函数:maxz=0.14x1+0.125x2+0.075x3约束方程为:X1+x2+x3<=0.8X1>=0.16X1<=0.32X2>=0.16X2<=0.4X3>=0.240.125x1+0.0875x2+0.0125x3=0.055X1,x2,x3>=0**********************最优解如下*************************目标函数最优值为:.08505变量最优解相差值-----------------------x1.160x2.2930x3.3470约束松弛/剩余变量对偶价格----------------------------10.06720-.013.1604.13305.10706.107070.667目标函数系数范围:变量下限当前值上限-------------------------------x1无下限.14.15x2.118.125.525x3.018.075.095常数项数范围:约束下限当前值上限-------------------------------1.709.81.62.089.16.2493.16.32无上限4无下限.16.2935.293.4无上限6无下限.24.3477.04.05.058<4>目标函数:maxz=0.18x1+0.125x2+0.075x3约束方程为:X1+x2+x3<=0.8X1-x2<=0X3>=0.24X1>=0.16X1<=0.32X2>=0.16X2<=0.40.125x1+0.0875x2+0.0125x3=0.05X1,x2,x3>=0**********************最优解如下*************************目标函数最优值为:.09294变量最优解相差值-----------------------x1.2130x2.2130x3.3730约束松弛/剩余变量对偶价格----------------------------10.06520.0123.10704.05305.18706.05307.133080.827目标函数系数范围:变量下限当前值上限-------------------------------x1.15.181.15x2无下限.125.145x3.018.075无上限常数项数范围:约束下限当前值上限-------------------------------1.682.81.62-.1330.0893.213.32无上限4无下限.16.2135.213.4无上限6无下限.16.2137无下限.24.3738.04.05.063分析总结:1.当单个基金预期收益率增加,单个投资分配额增加,相应的减少其他投资的资金额,投资总收益增加!2.当三个基金的预期收益率均增加,则需要在资金允许范围内,使每种基金的投资额达到最大,充分利用所有的投资基金!3.当单个基金预期收益率减小,但个基金投资分配额应该相应减少适当增加其他基金投资或者抽出多余资金用于其他用途!单个基金的收益率减小会较少投资总收益!4.当三个基金的预期收益率均减小,则投资基金投资总收益会相应的减少,因此要将每个投资的额度减小到可控范围内(总收益不变)的最小,多于资金用于其他投资!