# Problem 21

Algebra Level 5

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

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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