设变量x、y满足约束条件x≥1 、x+y-4≤0、x-y+1≤0,则目标函数z=3x-y的最大值是?

x+y-4≤0 x≤4-y
x-y+1≤0 x≤y-1
又x≥1,因此4-y≥1 y≤3 y-1≥1 y≥2
综上,得2≤y≤3
y-1≤4-y时,即2≤y≤2.5时,1≤x≤y-1
3-y≤3x-y≤3(y-1)-y 3-y≤3x-y≤2y-3 0.5≤3x-y≤2 0.5≤z≤2
y-1≥4-y时,即2.5≤y≤3时,1≤x≤4-y
3-y≤3x-y≤(4-y)-y 3-y≤4-2y y≤1,与2.5≤y≤3不符,因此无解.
综上,得0.5≤z≤2
z的最大值为2,最小值为0.5.