Consider the vectors: a 1 = ( 0 − 1 1 0 ) , a 2 = ( 0 0 − 1 1 ) , a 3 = ( 2 0 0 1 ) 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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Consider the vectors:      a    1    =      (                            0                                      −          1                                      1                                      0                      )    ,      a    2    =      (                            0                                      0                                      −          1                                      1                      )    ,      a    3    =      (                            2                                      0                                      0                                      1                      )  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&#039;t even seem possible to me that a single vector can maximize these three vectors.

eurgylchnj · Accepted Answer

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  .

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

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