The problem is: Given a total area, let's say, from (0,0) to (10,10); given an area for one point(x,y) that movable, let's say 2<=x<=6, 1<=y<=6. Find the closest position of (x,y) to the boundary of the total area. In the example, the solution should be (x,1), x can be any in the constraint.

Can this problem be solved in LP without binary condition?
Thanks.

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