for three variables, max f ( x , y , z ) = x y z s.t. ( x a ) 2 + ( y b ) 2 + ( z c ) 2 = 1where a , b , c are constanthow to solve the maximization optimization problem?thank you for helpin

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for three variables,  max  f  (  x  ,  y  ,  z  )  =  x  y  z    s.t.        (      x    a        )    2    +  (      y    b        )    2    +  (      z    c        )    2    =  1where   a  ,  b  ,  c are constanthow to solve the maximization optimization problem?thank you for helpin

thatuglygirlyu · Accepted Answer

One way is symmetrization via change of variable   s  =      x    a    ,  t  =      y    b    ,  u  =      z    c   and then optimize.  max  f  (  s  ,  t  ,  u  )  =  (  a  b  c  )  s  t  u      subject to:       s    2    +      t    2    +      u    2    =  1.. You can either use calculus or the fact that optimal point is of form   (  λ  ,  λ  ,  λ  ). Thus   s  =  t  =  u  =      1          3       so   (  x  ,  y  ,  z  )  =  (      a          3        ,      b          3        ,      c          3        ).In order to verify your answer you can use Hessian matrix (second derivative test)

for three variables, <mo movablelimits="true" form="prefix">max f ( x , y ,

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