So I'm trying to solve the following optimisation problem either theoretically or in MATLAB but not sure how to approach it. So I have the following function given by $$ z(x,y) = \frac{(-x-y-1) + xr + yr^{2} + r^{3}}{(x + 2y + 3)r^2} $$
and I need to find the lowest value of $z$, essentially optimise the parameters $x$ and $y$, such that roots of the cubic equation given by $ (-x-y-1) + xr + (y - z(x, y))r^{2} + r^{3}$ have absolute value less than $1$. I've tried the optimproblem function in MATLAB to help me solve the problem but haven't made any progress.