Lagrange Multipliers Method.
  Two dimentional case.
  

Drafts
   Multidimentional case ... 
   ... with little help of Linear Algebra.
   Following "Details" continue to describe this "idea" and do not
   pretend to be mathematically "strict":
   Consider the case when number of constrains m < n:
   Details 1
   Details 2
   Details 3
   Details 4