Algebra and Trigonometry 10th Edition

$0\lt x\lt100$
We know that $x+2y=100$, thus $y=50-0.5x$. The area is $x\cdot y=x(50-0.5x)=-0.5x^2+50x$. The domain of $x$ is $x\gt0$ and $50-0.5x\gt0\\50\gt0.5x\\100\gt x$. Thus $0\lt x\lt100$