Three. (16 points) A publishing company has set the following prices for a best-selling book:
$$
C(n)=\left\{\begin{array}{l}
12 n, \text { if } 1 \leqslant n \leqslant 24 ; \\
11 n, \text { if } 25 \leqslant n \leqslant 48 ; \\
10 n, \text { if } n \geqslant 49 .
\end{array}\right.
$$

Here $n$ represents the number of books ordered, and $C(n)$ is the amount of money (in yuan) paid for ordering $n$ books.
(1) For how many values of $n$ will buying more than $n$ books cost less than buying exactly $n$ books?
(2) If the cost of one book is 5 yuan, and two people come to buy books, with each buying at least one book and together buying 60 books, what is the minimum and maximum profit the publishing company can make?
(1) From $C(25)=275, C(24)=288, C(23)=$ 276, $C(22)=264$,
we have $C(25)<C(23)<C(24)$.
From $C(49)=490, C(48)=528, C(47)=517$,
$$
C(46)=506, C(45)=495, C(44)=484 \text {, }
$$

we have $C(49)<C(45)<C(46)<C(47)<C(48)$.
Therefore, there are 6 values of $n$ (i.e., $23,24,45,46,47,48$) where buying more than $n$ books costs less than buying exactly $n$ books.
(2) Let the two individuals buy $a$ and $b$ books respectively, and pay a total of $s$ yuan.
Assume $a \leqslant b$. From $a+b=60$ we know $1 \leqslant a \leqslant 30$.
$$
\begin{array}{l}
s=12 a+10 b=10(a+b)+2 a=600+2 a, \\
602 \leqslant s \leqslant 622 .
\end{array}
$$
(ii) When $12 \leqslant a \leqslant 24$, $36 \leqslant b \leqslant 48$,
$$
s=12 a+11 b=660+a, 672 \leqslant s \leqslant 684 \text {. }
$$
(iii) When $25 \leqslant a \leqslant 30$, $30 \leqslant b \leqslant 35$,
$$
s=11 a+11 b=660 \text {. }
$$

Therefore, the publishing company earns at least $602-60 \times 5=302$ (yuan), and at most $684-60 \times 5=384$ (yuan).