Valid sum over binary variables, basic question

**leoemil** · September 15th 2010, 03:48 PM

given the binary variables: y_i, x_i, i = 1,..,5
where
$ \sum_{i=1}^5 x_i = \sum_{i=1}^5 y_i = 1 $

Show that
$ \sum_{i=1}^t x_i \leq \sum_{i = 1}^{t} y_i, t \in \{1,\dots,5\} $
implies that:
$ \sum_{i=t}^5 x_i \geq \sum_{i = t}^{5} y_i, t \in \{1,\dots,5\} $

Can anybody help me, to show that it holds for every index?

**Ackbeet** · September 16th 2010, 02:25 AM

What is a "binary variable" in this case? What is the domain of such a variable? What kind of addition are you doing here?

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