# A perfect welcome to 2016

Algebra Level 5

$f(x,y,z,v,w)=xz+2yz+3zv+7zw$

Let $$M$$ be the maximal value of $$f$$ if $$x^2+y^2+z^2+v^2+w^2=2016$$ and all variables are positive. If $$M=f(x_0,y_0,z_0,v_0,w_0)$$, find $$w_0$$.

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