This is a very (very) basic problem, but I do not know how to proceed. In general, how to proceed when facing a system of nonlinear polynomial inequalities like this one?
\begin{equation*} \begin{cases} \alpha x + \beta xy + \gamma y \leq \delta,\\ x \geq 0 ,\\ x \leq 1,\\ y \geq 0 ,\\ y \leq 1,\\ \end{cases} \end{equation*}
Thanks a lot in advance for any feedback.