已知变量x,y满足约束条件y≤x,,x+y≤1,y≥-1,则目标函数z=2x+y的最大值
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y≤x (1')
x+y≤1 (2')
y≥-1 (3')
y=x (1)
x+y=1 (2)
y=-1 (3)
from (1) and (2)
B1(x,y)=(1/2, 1/2) satisfy (3')
from (1) and (3)
B2(x,y)=(-1,-1) satisfy (2')
from (2) and (3)
B3(x,y)=(2,-1) satisfy (1')
Z= 2x+y
Z(1/2,1/2) = 3/2
Z(-1,-1) = -3
Z(2,-1) = 3
max Z = Z(2,-1) = 3
x+y≤1 (2')
y≥-1 (3')
y=x (1)
x+y=1 (2)
y=-1 (3)
from (1) and (2)
B1(x,y)=(1/2, 1/2) satisfy (3')
from (1) and (3)
B2(x,y)=(-1,-1) satisfy (2')
from (2) and (3)
B3(x,y)=(2,-1) satisfy (1')
Z= 2x+y
Z(1/2,1/2) = 3/2
Z(-1,-1) = -3
Z(2,-1) = 3
max Z = Z(2,-1) = 3
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