# Consider the vectors: a 1 </msub> = ( <mtable rowspacing="4pt"

Consider the vectors:
${a}_{1}=\left(\begin{array}{c}0\\ -1\\ 1\\ 0\end{array}\right),{a}_{2}=\left(\begin{array}{c}0\\ 0\\ -1\\ 1\end{array}\right),{a}_{3}=\left(\begin{array}{c}2\\ 0\\ 0\\ 1\end{array}\right)$
Find a single vector $p$ which maximizes $p{a}_{i}$ for $i=1,2,3$.

To put this in context this is an economics profit max problem where p is a price and each component of the above vectors represents the quantity of the good.

I honestly have no idea how to find this p vector. It doesn't even seem possible to me that a single vector can maximize these three vectors.
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eurgylchnj
I think your question is incomplete. First you should determine your goal function, e.g., you can choose the sum of all profits to maximize, max: $p{a}_{1}+p{a}_{2}+p{a}_{3}$. Also you should determine your boundaries. E.g., total number of goods ${d}_{1},{d}_{2},{d}_{3},{d}_{3}$.