Square roots of variables?

Algebra Level 3

{a≤1a+b≤5a+b+c≤14a+b+c+d≤30 \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,ca,b,c and dd be positive real numbers satisfying the system of inequalities above. What is the maximum value of

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

Sharky Kesa by Sharky Kesa
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