A state highway department plan to construct a new road between two towns A and B.Town A lies on an abandoned road that runs east-west.Town B is 3 miles north of the point on that road that is 5 miles east of A.The engineering division proposes that the road be constructed by restoring a section of the old road from A up to point P and joining it to a new road that connects P and B.if the cost of restoring the old road is $200,000 per mile and the cost for the new road is $400,000 per mile,how much of the old road should be restored in order to maximize the department's costs?