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**razor****Member**- Registered: 2006-02-24
- Posts: 6

We have the real positive(only) numbers space of dimension two.

C={(x,y) belong to RxR and x+2*y<=2) and f(x,y)=min{x,y}.What is the minimum,x or y?

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

If you're looking for a definite answer, there isn't one.

if x > 2/3, y < x

if y > 2/3, x < y

Any other restrictions lead to arbitrary (unknown) results.

x + 2y <= 2

y <= -x/2 + 1

The way I thought about it was to first assume that x=y. Then 3y <= 2. So y <= 2/3. So if y increases any more, x must decrease. Even if y increases by a small amount, x must decrease by any small amount, and thus, x < y. The same is true for if x increases.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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