Answer
$1500$ units must be sold to gain a maximum profit of $\$7500$.
Work Step by Step
Let's compare $f(x)=-0.004x^2 + 12x-1500$ to $f(x)=ax^2+bx+c$. We can see that $a=-0.004, b=12, c=-1500$. $a\lt0$, hence the graph opens down, and so its vertex is a maximum. The maximum value is at $x=-\frac{b}{2a}=-\frac{12}{2\cdot(-0.004)}=1500.$ Hence, the maximum value is $f(1500)=-0.004(1500)^2 + 12(1500)-1500=7500.$
Thus, $1500$ units must be sold to gain a maximum profit of $\$7500$.
