I have the unknowns $w,x,y,z$ that are all in $\mathbb{N}$ and $\gt0$.
The known parameters $\alpha,\beta,\gamma,\delta$ are all in $\mathbb{N}$ and $\gt0$ too.
Given $\alpha,\beta,\gamma,\delta$, I need to find $w,x,y,z$ and these inequalities must be satisfied:
$\frac{w}{x+w}\leq\frac{1}{\alpha}$
$\frac{y}{y+z}\leq\frac{1}{\beta}$
$\frac{w+z}{x+y}\leq\frac{1}{\gamma}$
And also the following must be satisfied:
$w+x+y+z=\delta$
Is this problem solvable as an integer linear programming one?
Are the inequalities the constraints?
What is the objective function?
