若实数x,y满足x−y+1≥0x+y≥0x≤0
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若实数x,y满足
|
由实数x,y满足
x−y+1≥0
x+y≥0
x≤0,
作出可行域如图:
∵z=x+2y,解方程组
x−y+1=0
x+y=0,得A(-
1
2,
1
2),∴zA=-
1
2+2×
1
2=
1
2,
∵B(0,1),∴zB=0+2×1=2;
∴O(0,0),∴zO=0.
∴z=x=2y的最小值是0.
故答案为:0.
x−y+1≥0
x+y≥0
x≤0,
作出可行域如图:
∵z=x+2y,解方程组
x−y+1=0
x+y=0,得A(-
1
2,
1
2),∴zA=-
1
2+2×
1
2=
1
2,
∵B(0,1),∴zB=0+2×1=2;
∴O(0,0),∴zO=0.
∴z=x=2y的最小值是0.
故答案为:0.
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