Question: Strange Optimization Output

Hello everyone

I observe the following "strange" case and I am wondering if I am missing something. So, any insights are more than appreciated. The case is the followin:

When I use

Interactive(x + y, {x = 0 .. 1, y = 0 .. 1, 1 <= x + y})

I get: objective =1, x=y=.5

However, If I run

Minimize(x + y, {x >=0,x<=1, y>=0,y<=1, 1 <= x + y})

then I get: objective =1, x=1, y=0

Why there is such a difference? Because of there are multiple solutions? 

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