One, (20 points) As shown in Figure 3, goods are to be transported from a riverside city $A$ to a location $B$ 30 kilometers away from the riverbank. According to the distance along the river, the distance from $C$ to $A$, $AC$, is 40 kilometers.
If the waterway transportation cost is half of the highway transportation cost, how should the point $D$ on the riverbank be determined, and a road be built from $B$ to $D$, so that the total transportation cost from $A$ to $B$ is minimized?
Let the waterway transportation cost per kilometer be 1, and let $AD$ be $x$ kilometers, then $DC$ is $40-\pi$ kilometers. Since the highway transportation cost per kilometer is twice that of the waterway per kilometer, according to the problem, the total cost is
$$
y=x+2 \sqrt{(40-x)^{2}+30^{2}} \text {. }
$$

Simplifying, we get $3 x^{2}-2(160-y) x+\left(10000-y^{2}\right) \geqslant 0$.
Solving this inequality, we get
$$
y \leqslant 40-30 \sqrt{3} \text { (discard) }
$$

or $y \geqslant 40+30 \sqrt{3}$.
Therefore, the minimum value of $y$ is $40+30 \sqrt{3}$.
Substituting into (1), we get
$$
x=40-10 \sqrt{3} \approx 23 \text {. }
$$

Thus, point $D$ should be approximately 23 kilometers from $A$ on the riverbank, which will minimize the transportation cost.