The Newisham Reservoir
Newisham has a population of about 30,000. It traditionally got its water supply from the nearby River Feltham but increasing quantities of water were being extracted from the river by industry upstream. When the flow reaching the Newisham water treatment works became too small to supply the town's needs, the council decided to build a reservoir by damming the Feltham and diverting tributaries. This work was finished in 2002 and gave a guaranteed supply of water to the town. Unfortunately, the dam reduced the amount of water available to farmers downstream, and two of them recently found the water supply to their cattle had effectively dried up. The farmers now face the option of either connecting to the local mains water supply at a cost of £44,000 or drilling a new well. The drilling company cannot give an exact cost for the work but suggest guidelines of £32,000 (with a probability of 0.3), £44,000 (with a probability of 0.3) or £56,000, depending on the underground rock structure and depth of water. A local water survey company can do some more onsite tests. For a cost of £600 they will give either a favourable or an unfavourable report on the chances of easily finding water. The reliability of this report (phrased in terms of the probability of a favourable report, given that the drilling cost will be low etc.) is given in this table:
Questions
1. What would a decision tree of the farmers' problem look like?
2. What are their best choices and expected costs?