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Trying to understand the example of Chvatal-Gomory cutting planes (Lee p. 153), they say:

$\max 2x_1 + x_2 $
subject to:
$7x_1 + x_2 \leq 28$
$-x_1 +3x_2 \leq 7$
$-8x_1 -9x_2 \leq -32 $
$x_1, x_2 \geq 0$
$x_1, x_2 \in \mathbb{Z}$

The choice of $u_1=0$, $u_2=1/3$, $u_3=1/3$ yields the cutting plane $-3x_1 - 2x_2 \leq -9$. The choice of $u_1 = 1/21$, $u_2=7/22$, $u_3=0$ yields the cutting plane $x_2\leq 3$.

But have no idea how they made that "choice" for the u's! Is it just a guess?

Any tips appreciated!

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Yes, it is just a guess. The topic of "how" to choose them is covered later in the book, like in the next chapter.

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