A.14 B.16

C.17 D.19

解析:画出不等式组{■(x+2y"-" 5>0@2x+y"-" 7>0@x≥0"," y≥0)┤表示的平面区域,如图中阴影部分所示.

　　因为x,y为整数,所以z=3x+4y在点A(4,1)处取到最小值16.

答案:B

5.设变量x,y满足|x|+|y|≤1,z=2x+y,则z的最大值和最小值分别为(　　)

A.1,-1 B.2,-2 C.1,-2 D.2,-1

解析:|x|+|y|≤1表示的平面区域如图阴影部分所示.

　　当直线y=-2x+z过点(1,0)时,z最大;当直线y=-2x+z过点(-1,0)时,z最小,则z的最大值为2,最小值为-2.

答案:B

6.设变量x,y满足约束条件{■(x"-" 2≤0"," @x"-" 2y≤0"," @x+2y"-" 8≤0"," )┤则目标函数z=3x+y的最大值为(　　)

A.7 B.8 C.9 D.14

解析:画出题中约束条件满足的可行域,如图中阴影所示.

　　目标函数z=3x+y可化为y=-3x+z,平移目标函数线当其过点A时,z取最大值.由{■(x=2"," @x+2y"-" 8=0)┤得{■(x=2"," @y=3"." )┤

　　所以点A的坐标为(2,3),zmax=3×2+3=9.

答案:C

7.若实数x,y满足不等式组{■(x+y≥2"," @2x"-" y≤4"," @x"-" y≥0"," )┤则z=2x+3y的最小值是　　　　　.

解析:画出可行域如图阴影部分所示.