Let $f(x, y, z)=x z+y z$. Using Lagrange multipliers, find the location(s) and value of the maximum of $f$ on the intersection of the unit sphere $\left(x^{2}+y^{2}+z^{2}=1\right)$ and the ellipsoid given by $\frac{1}{4} x^{2}+\frac{1}{4} y^{2}+4 z^{2}=1$.