30. Consider a triangle $A B C$, where $A B=20, B C=25$ and $C A=17$. $P$ is a point on the plane. What is the minimum value of $2 \times P A+3 \times P B+5 \times P C$ ?
30. Answer: 109.
$$
2 \cdot P A+3 \cdot P B+5 \cdot P C=2(P A+P C)+3(P B+P C) \geq 2 \cdot A C+3 \cdot B C=2 \cdot 17+3 \cdot 25=109
$$

The equality holds if and only if $P=C$.