A man is on an Island, 4 km from the nearest point P, on a straight shore. He wants to connect a cable from his present position to a point B , on the shore that is 9000 meters from P. The cable costs $5 per meter in the water and costs $3 per meter on shore. Where on the shore should the cable exit the water, so that the cable costs the least amount of money?
Trigonometry and derivatives are used to minimize distance. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.