mathematical optimization - Easy FindMaximum returns a wrong answer

FindMaximum in region is a new function in mma10,but when I tried the following example:

region = Polygon[{{0, 0}, {10, 0}, {10, 5}, {5, 5}, {5, 10}, {0, 10}}]
FindMaximum[{x + y, {x, y} \[Element] region}, {x, y}]

Mathematica 10.1 returns

{10., {x -> 5., y -> 5.}}

We can easily know that it is wrong. What's the story?

Answer

Defining just one of the points of the region with a decimal point helps, suggesting that the method chosen by FindMaximum for integer coordinates is a perhaps a linear programming method, and gets stuck at the observed {5, 5}.

Instead one can do:

region = Polygon[{{0., 0}, {10, 0}, {10, 5}, {5, 5}, {5, 10}, {0, 
     10}}];
result = Last@FindMaximum[{x + y, {x, y} \[Element] region}, {x, y}]
(* {x -> 10., y -> 5.} *)

Show[ContourPlot[x + y, {x, y} \[Element] region], 
 Graphics[{Red, PointSize[Large], Point[{x, y} /. result]}]]

enter image description here

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