Minimizing the cost of cable across a river
A power plant sits on the bank of a river, and must be connected by cable to a relay station on the other side. The cheapest way to connect them would be in a straight line, if it weren't for the fact that the part of the cable that crosses the water has a different cost than the part that crosses land.
In the situation shown below, you can change how much more expensive river-crossing cable is, compared to land-crossing cable. The red point on the bank of the river (where the two types of cable meet) can be dragged and you can observe how its position affects the total cable cost.