3. 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, each buying at least 1 book, and together they buy 60 books, what is the minimum and maximum profit the publishing company can make?
3. (1) From $c(25)=275, c(24)=288, c(23)=276, c(22)=264$, we have $c(25)<c(23)<c(24)$; from $c(49)=490, c(48)=528, c(47)=517, c(46)=506, c(45)=495, c(44)=484$, we have $c(49)<c(45)<c(46)<c(47)<c(48)$. Therefore, there are 6 values of $n$ (i.e., $23, 24, 25, 46, 47, 48$) where buying more than $n$ books costs less than buying exactly $n$ books;
(2) Let the two individuals buy $a$ and $b$ books respectively, paying a total of $S$ yuan. Without loss of generality, assume $a \leqslant b$, and from $a+b=60$ we know $1 \leqslant a \leqslant 30$.
(1) When $1 \leqslant a \leqslant 11$, $49 \leqslant b \leqslant 59$, $S=12a+10b=600+2a$, so $602 \leqslant S \leqslant 622$;
(2) When $12 \leqslant a \leqslant 24$, $36 \leqslant b \leqslant 48$, $S=12a+10b=660+a$, so $672 \leqslant S \leqslant 684$;
(3) When $25 \leqslant a \leqslant 30$, $30 \leqslant b \leqslant 35$, $S=11a+11b=660$.
Thus, the publishing company earns at least $602-60 \times 5=302$ (yuan) and at most $684-60 \times 5=384$ (yuan).