13.18 If $a<b<c, x<y<z$, which of the following four algebraic expressions:

甲: $a x+b y+c z$. 乙: $a x+b z+c y$.
丙: $b x+a y+c z$. 丁: $b x+c y+a z$.
is the largest one?
(A) It must be 甲.
(B) It must be 乙. (C) It must be 丙.
(D) It must be 丁 (Shanghai Junior High School Mathematics Competition, 1983; Fujian Junior High School Mathematics Competition, 1984)
[Solution] For 甲 $-乙=(b-c) y+(c-b) z=(b-c)(y-z)>0$,
$$
\begin{array}{l}
\therefore \text { 甲 }>\text { 乙; } \\
\text { 甲 - 丙 }=(a-b) x+(b-a) y=(a-b)(x-y)>0 \text {, } \\
\therefore \text { 甲 }>\text { 丙; } \\
\text { 丙 - 丁 }=(a-c) y+(c-a) z=(a-c)(y-z)>0 \text {, } \\
\end{array}
$$
$$
\therefore \text { 丙 }>\text { 丁, i.e., 甲 }>\text { 丁. }
$$

Therefore, the correct choice is $(A)$.