## Binary Integer Programming Problem

Hi,

Below I need solve for the binary variables $x_1,x_2,y_1,y_2,z_1,z_2$ that minimize the functions $f(x), f(y), f(z)$, subject to the 5 constraints that follow. By binary I mean they can only be 1 or 0.

I appreciate any advice as to what sort of strategy I might use. Thanks.

$x_1u_{1}+x_1u_{2}-h=f(x)$
$y_1u_{1}+y_1u_{2}-h=f(y)$
$z_1u_{1}+z_1u_{2}-h=f(z)$

$s.t.$
$x_1+x_2\leq1$
$y_1+y_2\leq1$
$z_1+z_2\leq1$
$x_1+y_1+z_1=1$
$x_2+y_2+z_2=1$