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

Jaydan Aguirre 2022-07-09 Answered
for three variables,
max f ( x , y , z ) = x y z s.t.     ( x a ) 2 + ( y b ) 2 + ( z c ) 2 = 1
where a , b , c are constant
how to solve the maximization optimization problem?
thank you for helpin
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Answers (1)

thatuglygirlyu
Answered 2022-07-10 Author has 14 answers
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)

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