当直线l经过点B(1,1)时,zmin=2×1-2×1+4=4.

★11.求z=5x-8y的最大值,式中的x,y满足约束条件{■(x+y≤6"," @5x+9y≤45"," @x≥0"," @y≥0"." )┤

解:作出满足不等式组{■(x+y≤6"," @5x+9y≤45"," @x≥0"," @y≥0)┤的可行域,如图阴影部分所示.

　　作直线l0:5x-8y=0,平移直线l0,由图可知,当直线平移到经过点A时,z取最大值.解方程组{■(x+y=6"," @y=0"," )┤得A(6,0),所以zmax=5×6-8×0=30.

★12.若实数x,y满足不等式组{■(2≤2x"-" y≤4"," @x≤3"," @y≥"-" 3"," )┤求下列目标函数的最大值,以及此时x,y的值.

(1)z=x-y;

(2)z=x+3y+1.

解:在平面直角坐标系中画出可行域,如图阴影部分所示.

　　 (1)当直线y=x-z移动到经过点A(1/2 ",-" 3)时,直线在y轴上的截距-z最小,为-7/2,所以当x=1/2,y=-3时,z取得最大值7/2.

　　(2)当直线y=-1/3x+(z"-" 1)/3移动到经过点B(3,4)时,直线在y轴上的截距(z"-" 1)/3最大,为5,所以当x=3,y=4时,z取得最大值16.