15. A 33-story building has an elevator that starts on the first floor. It can accommodate a maximum of 32 people and can only stop once at one of the floors from the 2nd to the 33rd. For each person, walking down one floor of stairs results in 1 point of dissatisfaction, and walking up one floor of stairs results in 3 points of dissatisfaction. Now, there are 32 people on the first floor, and they each live on one of the floors from the 2nd to the 33rd. Question: On which floor should the elevator stop to minimize the total dissatisfaction score of these 32 people? What is the minimum value? (Some people can choose to walk up the stairs instead of taking the elevator).
15. It is easy to see that these 32 people live on each of the 2nd to 33rd floors, one person per floor. For each person who takes the elevator to go up or down, the floor they live on must be no less than the floor of the person who walks up directly. In fact, if a person living on the $s$-th floor takes the elevator, and a person living on the $t$-th floor walks up directly, with $s < t$, swapping their methods of going up, while keeping the others unchanged, will reduce the total dissatisfaction score.

Let the elevator stop at the $x$-th floor, and $y$ people on the first floor do not take the elevator but walk up directly. Then, the total dissatisfaction score is
$$
\begin{aligned}
S= & 3[1+2+\cdots+(33-x)]+3(1+2+\cdots \\
& +y)+[1+2+\cdots+(x-y-2)] \\
= & \frac{3 \times(33-x)(34-x)}{2}+\frac{3 y(y+1)}{2} \\
& +\frac{(x-y-2)(x-y-1)}{2} \\
= & 2 x^{2}-x y-102 x+2 y^{2}+3 y+1684 \\
= & 2 x^{2}-(y+102) x+2 y^{2}+3 y+1684 \\
= & 2\left(x-\frac{y+102}{4}\right)^{2}+\frac{1}{8}\left(15 y^{2}-180 y+3068\right) \\
= & 2\left(x-\frac{y+102}{4}\right)^{2}+\frac{15}{8}(y-6)^{2}+316 \\
\geqslant & 316 .
\end{aligned}
$$

Furthermore, when $x=27, y=6$, $S=316$.
Therefore, when the elevator stops at the 27th floor, the total dissatisfaction score is minimized, with the minimum value being 316 points.
(Note: Directly providing the correct answer earns 5 points.).
(Provided by Qiao Yu)