Suppose that f ( ⋅ ) is a quadratic and concave function such that it has a maximum, x ∈ R , y ∈ ( 0 , + ∞ ). I have to solve a maximization problem that is max x y f ( x / y )My question is that, since I want to maximize with respect to x / y, I will treat this as if ∂ f ( x / y ) ∂ ( x / y ) ?Or do i need to maximize with respect to x, then in y and use the Hessian matrix?Or is it something else? Well it is a composition of functions after all, isn't it? I am a llitle confused...

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Suppose that   f  (  ⋅  ) is a quadratic and concave function such that it has a maximum,   x  ∈      R  ,   y  ∈  (  0  ,  +  ∞  ). I have to solve a maximization problem that is      max                            x          y                      f  (  x      /    y  )My question is that, since I want to maximize with respect to   x      /    y, I will treat this as if             ∂      f      (      x              /            y      )              ∂      (      x              /            y      )      ?Or do i need to maximize with respect to   x, then in   y and use the Hessian matrix?Or is it something else? Well it is a composition of functions after all, isn&#039;t it? I am a llitle confused...

Turynka2f · Accepted Answer

Suppose   a is the point where   f is maximal, then, all the couples   (  x  ,  y  ) that verify   x      /    y  =  a are solutions to the optimization problem.

Suppose that f ( ⋅ ) is a quadratic and concave function such that i

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