Given the following constrained problem:
ext{max} (x-1)^2 + (y-1)^2 + xy
x^2 + y^2 \leq 200
x \geq 0
y \geq 0

Question

Given the following constrained problem: 
   	ext{max} (x-1)^2 + (y-1)^2 + xy  
   x^2 + y^2 \leq 200  
  x \geq 0  
  y \geq 0

Accepted Answer

Point (x=10, y=10) is a feasible point that satisfies the first-order necessary and not second-order sufficient conditions, so I cannot claim that it is a global maximum.

Answer

Point (x=0, y=0) is the global maximum because, although it does not satisfy the first-order necessary condition, it is a vertex of the feasible region.

Answer

Point (x=0, y=0) is a feasible point that satisfies the second-order sufficient condition but not the first-order necessary condition, so it is a stationary point.

Answer

Point (x=10, y=10) is a feasible point that satisfies the first-order necessary and second-order sufficient conditions for being a global maximum.

Crowdly

Given the following constrained problem: \text{max} (x-1)^2 + (y-1)^2 + xy ...

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