Question

若实数x,y满足x>=0，y>=0，x+y<=1,则z=3x+y的最大值为

麻烦写上过程

Answer 1

x+y<=1
x<=1-y

z=3x+y=3(1-y)+y=3-3y+y=3-2y
因为y>=0
2y>=0
-2y<=0
所以
z<=3-2y<=3
所以最大值为3

Answer 2

解 ∵ x+y<=1
∴ x<=1-y
z=3x+y<=3(1-y)+y=3-3y+y=3-2y
因为y>=0
2y>=0
-2y<=0
所以
z<=3-2y<=3
即 z的最大值为3