An electric company wishes to lay a cable from point $A$ on an island $10$ kilometers offshore to point $B$ on the coast $20$ kilometers from the point, $C$, on the shore nearest the island. If it costs $5$ per kilometer to run the cable underwater and $4$ per kilometer to run the cable on land, find the point, $D$ (between $B$ and $C$), to which the cable should be run from $A$ and then to $B$ in order to minimize the cost?
I have tried solving the question, but I am ending up with a negative solution. I can't find my mistake(my solution is attached as an imagine) Thank you, everyone, for your precious time!
