Summation Summation Summation
Algebra
Level
4
Given \(x_k, y_k, z_k > 0 \) for all \(k\) satisfy the three summations:
\[ \begin{eqnarray} \displaystyle \sum_{k=1}^{2015} x_k & = & 50 \\ \displaystyle \sum_{k=1}^{2015} y_k & = & 169 \\ \displaystyle \sum_{k=1}^{2015} z_k & = & 961 \\ \end{eqnarray} \]
What is the minimum value of \( \displaystyle \sum_{k=1}^{2015} \left ( x_k y_k z_k \right ) \)?
by
Jason Hughes