运筹学案例(11)

案例

Xi

0，不给A,B,C,D,E五个项目投资，

i 1,2,3,4,5

1，给A,B,C,D,E五个项目投资，

则99年初可投资金额为280000+Y1

99年底可收益的金额为55000X1+30000X2+70000X4+32500X5+1.1M1-1.12Y1 00年初的可投资金额为

（55000X1+30000X2+70000X4+32500X5+1.1M1-1.12Y1）+M2 00年底可收益的金额为

75000X1+100000X2+120000X3+67000X5+1.1M2-1.12Y2

01年初可投资金额为

（75000X1+100000X2+120000X3+67000X5+1.1M2-1.12Y2）+M3

01年底可收益金额为

95000X1+73000X2+40000X3+84000X4+50000X5+1.1M3-1.12Y3 因此，目标函数为：

Max Z= 95000X1+73000X2+40000X3+84000X4+50000X5+1.1M3-1.12Y3 约束条件：

106250X1+95000X2+64000X3+50000X4+56000X5+M1=280000+Y1

37500X1+15000X2+24000X3+25000X4+42000X5+M2=

（55000X1+30000X2+70000X4+32500X5+1.1M1-1.12Y1）+Y2

43750X1+30000X2+12000X3+35000X4+32000X5+M3=

75000X1+100000X2+120000X3+67000X5+1.1M2-1.12Y2）+Y3

25X1+20X2+40X3+20X4+65X5 120

X5=1

106250X1+95000X2+640000X3+50000X4+56000X5 371250 37500X1+15000X2+24000X3+25000X4+42000X5 143500 43750X1+30000X2+12000X3+35000X4+32000X5 152750 55000X1+30000X2+70000X4+32500X5 187500 75000X1+100000X2+120000X3+67000X5 362000

95000X1+73000X2+40000X3+84000X4+50000X5 342000

其中Xi为0---1 变量;Xi≥0, Yj≥0; i=1,2,3,4,5; j=1,2,3;

用管理运筹学软件求其结果，则有：

Y1=X6， Y2=X7， Y3=X8 , M1=X9 , M2=X10 ， M3=X11