Below I need solve for the binary variables $\displaystyle x_1,x_2,y_1,y_2,z_1,z_2$ that minimize the functions $\displaystyle f(x), f(y), f(z)$, 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.

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

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