Consider three vectors $\mathbf{u} = \begin{pmatrix} 2 \\ 4 \\ 6 \end{pmatrix}$, $\mathbf{v} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}$, and $\mathbf{w} = \begin{pmatrix} 4 \\ 8 \\ 12 \end{pmatrix}$. Determine if the vectors are collinear. If so, find the total cost to purchase 15 units of a product, given that a single unit costs $8 each, but if you buy a bulk of 5 units, the cost is $35. Let's think step by step and output the final answer within \boxed{}.
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