Restrict a free parameter to feasible donor counts

Let $x,y,z$ be the numbers of type A, B and O donors. Then $x+y+z=1200$ and $0.35x+0.40y+0.45z=520$. The printed calculator result is $x=-800+z$, $y=2000-2z$, $z=z$.

All three counts must be nonnegative integers. From $x=z-800\ge0$, $z\ge800$; from $y=2000-2z\ge0$, $z\le1000$. Hence every integer $z$ from 800 to 1000 inclusive is possible. At $z=800$, $(x,y,z)=(0,400,800)$; at $z=1000$, it is $(200,0,1000)$. The formulas produce valid integer counts throughout that interval.

The lecturer asks for an assumption: each donor can donate the required volume according to their blood type. The per-type volumes are fixed by the stated model. The equations and range depend on that assumption; the mathematical problem is not a claim about actual donation practice.