Question 7
Find the maximal value of
$$
S=\sqrt[3]{\frac{a}{b+7}}+\sqrt[3]{\frac{b}{c+7}}+\sqrt[3]{\frac{c}{d+7}}+\sqrt[3]{\frac{d}{a+7}}
$$
where $a, b, c, d$ are nonnegative real numbers which satisfy $a+b+c+d=100$.
$$
S=\sqrt[3]{\frac{a}{b+7}}+\sqrt[3]{\frac{b}{c+7}}+\sqrt[3]{\frac{c}{d+7}}+\sqrt[3]{\frac{d}{a+7}}
$$
where $a, b, c, d$ are nonnegative real numbers which satisfy $a+b+c+d=100$.