  We study an optimal stretching problem for certain convex domain in
$\mathbb{R}^d$ ($d\geq 3$) whose boundary has points of vanishing Gaussian
curvature. We prove that the optimal domain which contains the most positive
(or least nonnegative) lattice points is asymptotically balanced. This type of
problem has its origin in the "eigenvalue optimization among rectangles"
problem in spectral geometry. Our proof relies on two-term bounds for lattice
counting for general convex domains in $\mathbb{R}^d$ and an explicit estimate
of the Fourier transform of the characteristic function associated with the
specific domain under consideration.
