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A state highway department plans to construct a new road between two towns A and B. Town A lies on an abandoned road that runs east-west.
A state highway department plans 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 minimize the department's costs?
