The town of Foxton lies 10 mi north of an abandoned east-west road that runs through Grimley, as shown in the figure. The point on the abandoned road closest to Foxton is 30 mi from Grimley. County officials are about to build a new road connecting the two towns. They have determined that restoring the old road would cost $100,000 per mile, while building a new road would cost $200,000 per mile. How much of the abandoned road should be used (as indicated in the figure) if the officials intend to spend exactly $5.8 million?