Question

若X Y 满足X+2Y小于等于4,X -Y小于等于1,X + 2大于等于零,则Z = 3X - Y 的最大值?

Answer 1

x+2≥0 x≥-2

x-y≤1 x≤y+1

-2≤x≤y+1

y+1≥-2

y≥-3

x+2y≤4

-2+2y≤x+2y≤y+1+2y≤4

x取最大值y+1,x+2y≤4成立

3y+1≤4

y≤1

-3≤y≤1

z=3x-y

-2-y≤z≤3(y+1)-y=2y+3

z≤2+3=5

z的最大值为5.