VN-TST 2001 Problem 4

Let's consider the real numbers $a, b, c$ satisfying the condition

$$21 \cdot a \cdot b + 2 \cdot b \cdot c + 8 \cdot c \cdot a \leq 12.$$

Find the minimal value of the expression

$$P(a, b, c) = \frac{1}{a} + \frac{1}{b} + \frac{1}{c}.$$