1）∵x,y∈[0,50]
∴50-x≥0,50-y≥0
x/(x+y)≤1①(y=0时等号成立)
(50-x)/[100-(x+y)]=(50-x)/[(50-x)+(50-y)]≤1②(y=50时等号成立)
∵①,②等号不能同时成立
∴x/(x+y)+(50-x)/[100-(x+y)][x+(50-x)]/{(x+y)+[(50-x)+(50-y)]}
=50/100=1/2
综上得：1/2
1）∵x,y∈[0,50]
∴50-x≥0,50-y≥0
x/(x+y)≤1①(y=0时等号成立)
(50-x)/[100-(x+y)]=(50-x)/[(50-x)+(50-y)]≤1②(y=50时等号成立)
∵①,②等号不能同时成立
∴x/(x+y)+(50-x)/[100-(x+y)][x+(50-x)]/{(x+y)+[(50-x)+(50-y)]}
=50/100=1/2
综上得：1/2