当直线y=-2/3x+z过点A(2,0)时,z=2x+3y有最小值4.

答案:4

8.若实数x,y满足{■(y≤2x"," @y≥"-" 2x"," @x≤3"," )┤则目标函数z=x-2y的最小值是　　　　　.

解析:

画出满足不等式组的可行域如图阴影部分所示,目标函数化为y=1/2x-z,当直线经过点A时,-z的值最大,z的值最小,点A坐标为(3,6),所以z的最小值为3-2×6=-9.

答案:-9

9.若x,y满足不等式组{■(x"-" y+1≥0"," @x+y+1≥0"," @x+2y"-" 2≤0"," @x"-" 2y"-" 2≤0"," )┤则z=3x+y-7的最大值为　　　　　.

解析:画出可行域如图阴影部分所示.

　　当直线y=-3x+z0经过点A(2,0)时,直线在y轴上的截距z0最大,所以z0=3x+y有最大值6,故z=3x+y-7有最大值-1.

答案:-1

10.设z=2y-2x+4,式中x,y满足{■(0≤x≤1"," @0≤y≤2"," @2y"-" x≥1"," )┤求z的最大值和最小值.

解:作出满足不等式组{■(0≤x≤1"," @0≤y≤2"," @2y"-" x≥1)┤的可行域,如图阴影部分所示,作直线l:2y-2x=z-4,当直线l经过点A(0,2)时,zmax=2×2-2×0+4=8;