[Help-glpk] Can this problem be solved in LP without binary condition?

[xm]

 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.