已知变量xy满足-1<=x+y<=y。且2<=x-y<=3,则z=2x-3y的取值范围是?

2025-05-14 17:08:43
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回答1:

把X+Y和X-Y看成两个基本量,则Z=2X-3Y可变形为Z=-0.5(X+Y)+2.5(X-Y),由X+Y和X-Y的取值范围可知,-2<-0.5(X+Y)<0.5, 5<2.5(X-Y)<7.5,由此得,Z=2X-3Y的范围为3<Z<8