Explanation

(c)
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$\geq 15\sqrt{\left( \frac{2p}{3} \right)^{3}\left( \frac{3q}{5} \right)^{5}\left( \frac{4r}{7} \right)^{7}\ }$ $(\because AM \geq GM)$
$\Rightarrow \ \ p^{3}q^{5}r^{7}\ \frac{2^{3}3^{5}4^{7}}{3^{3}5^{5}7^{7}} \leq 1$
$\Rightarrow \ \ p^{3}q^{5}r^{7} \leq \frac{5^{5}\ 7^{7}}{2^{3}\ 3^{2}\ 4^{7}}$