Answer
See below.
Work Step by Step
Let's compare $f(x)=-0.5x^2+1900x$ to $f(x)=ax^2+bx+c$. We can see that a=-0.5, b=1900, c=0. $a\lt0$, hence the graph opens down, hence its vertex is a maximum. The maximum value is at $x=-\frac{b}{2a}=-\frac{1900}{2\cdot(-0.5)}=1900.$ Hence the maximum value is $f(1900)=-0.5(1900)^2+1900(1900)=1805000.$