Consider a 8km by 10km square lake with corners given by coordinates (0,0), (8, 0), (0, 10), (8, 10).
In the corner of the lake containing (0,0), there is a patch of fog which is 4km by 4km. A boat starts
at (0,0) and wants to travel to (8, 10). The boat will travel in a straight line until the boundary
of the fog, possibly change direction, and then travel in a straight line again until it reaches (8, 10).
The boat can travel 1km per minute in the fog and 2km per minute outside of the fog. The boat
captain wants to reach (8, 10) as fast as possible. Write an NLP formulation for this problem. Note,
in our definition of an NLP you cannot write explicitely the condition that a variable needs to take
an integer value.