Square roots of variables?

Algebra Level 3

\[ \begin{cases} a \leq 1 \\ a+b \leq 5 \\ a+b+c \leq 14 \\ a+b+c+d \leq 30 \end{cases} \]

Let \(a,b,c\) and \(d\) be positive real numbers satisfying the system of inequalities above. What is the maximum value of

\[ \sqrt{a} + \sqrt{b} + \sqrt{c} + \sqrt{d} \quad ? \]

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