Suppose A is a $5\backslash$times $10$ integer matrix, and b in Z$5$ and c in Z$10$ are integer vectors. Consider the integer

program

max $\{$cT x : Ax $=$ b$,$ x $>=0,$ x in Zn$\}($IP$)$

Let $($P$)$ be the LP relaxation of $($IP$).$ Suppose that B $=\{1,2,3,4,5\}$ is an optimal basis for $($P$),$ that

$$x is the corresponding basic feasible solution, and that the canonical form for $($P$)$ with respect to B

includes the following constraint:

x$1+1$

$2$ x$6+0$x$71$

$3$ x$81$

$4$ x$9+0$x$10=5$

$2$

Prove that

x$6+$ x$8+$ x$9>=1$

is a cutting plane for $$