Optimization - Getting Power to an Island


The residents of an island 4 km from the shore want to get power from a power station that is 10 km down the shore line. They must lay wire under water to some point on the shore, then they can run wire from that point along the shore to the power station.


  1. Using the sliders you can change the cost for laying wire on water and land, and see how this affects the total cost of the project.
  2. Next, move the blue point on the shore, to see how the total cost for the project changes. Find the point on the shore that minimizes the total cost of the project.
  3. Under what circumstances will the minimal cost be achieved by laying the wire entirely under water from the island to the power station?
  4. Reset the applet to its initial condition (the icon in the top right corner).
    1. Experimentally, find the point on the shore that minimizes total cost.
    2. Use calculus to find the exact point that minimizes cost, and figure out what that cost will be. (Be careful with units, since both meters and kilometers are used.)
    3. Do your two answers agree?