In 2009 Canadian Renewable Energy Corporation (CREC) connected its Wolfe Island Wind Farm to the Ontario electric power grid and now delivers about 594 gigawatt-hours (GW•h) of renewable energy annually. One of the issues in the development of this project was the route of the cable to take power from CREC's collector substation on the island across to the mainland at Kingston. This involved the laying of both land cable on Wolfe Island and a water cable across the channel between the island and Kingston.
The point at which the cable would come ashore at Kingston was dictated by the location of an existing Hydro One transformer station, but CREC had some choice concerning the point on Wolfe Island where the cable could enter the water. Since laying cable is costly on land or in water, but more so in water, CREC wished to determine the least expensive route. The costs per km of laying the cable were $20.5M on land and $31.4M in the water. How could CREC determine the best route and what would this minimum cost be?
The GeoGebra applet below can help you investigate the cost of the cable for the various route options. Drag the purple point along the east-west shoreline to examine the possible paths for the cable. The graph generated is a plot of the distance the point of entry into the water is from point E on the shore versus the resulting cable cost.
The applet holds all the GeoGebra tools and can be used to help you answer the questions below.

1. What is the shape of the curve (Cost Curve) generated when you select different cable routes by dragging the purple point?
2. Looking at the graph locate the minimum cable cost and the point along the WE line that generates the cable path with this cost.
3. What type of function might fit this Cost Curve?
4. Open the Algebra View in the applet and build a function that passes through the Cost Curve points.
5. Use the Two Variable Regression Analysis tool in the SpreadSheet View to construct a function model for the Cost Curve.
6. Open the CAS View in the applet and use the tools there to locate the point on the WE line that generates the least cost.