A lighthouse, L, is located on a small island 4 km west of point A on a straight north-south coastlne. A power cable is to be laid from L to the nearest source of power at point B on the shoreline, 12 km north of point A. The cost of laying cable under water is $6000/km and the cost of laying cable along the shoreline is $2000/km. To minimize the cost, the power line will be built from L underwater to a point C on the shoreline and then alone the shoreline from C to B. Find the location of point C (to the nearest metre) on the shoreline where the power cable should enter the water.