A public works department is to construct a new road between towns A and B. Town A lies...

A public works department is to construct a new road between towns A and B. Town A lies on an abandoned road running east–west. Town B lies20 miles north of this road and 40 miles east of town A. An engineer proposes that the road be constructed by restoring a section of the old road leaving town A and joining it to an entirely new section of road at a point to be determined, connecting that point with town B (see the figure).

a. If the cost of restoring the old road is $200,000 per mile and the cost of new construction is $400,000 per mile, determine the function describing the total cost.

b. Estimate how much of the old road should be restored in order to minimize the department’s cost.