Problem 21

$\large \frac{1}{H}+\frac{2}{K}+\frac{3}{A}$

Let $H,K$ and $A$ be positive reals satisfying $21HK+2KA+8AH\leq 12$ .

Let the minimal value of the expression above is $M$ and the sum of $H,K,A$ when the equality holds be $S$ . Compute $\left \lceil M+S \right \rceil$ .

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This problem was in Vietnam TST a few year back.

This problem is in this Set .