operation research

1. Buy or Drill Problem A farmer Fliving in a water scarce region is faced with the problem of whether she/he should drill a well in his farm, or continue to buy water from her/his neighbour N to meet their irrigation requirements. The life of a new well is estimated to be ten years. F has estimated that the total cost of buying water from N over the ten years would be Rs 20,000. The cost of drilling a well would be Rs 50 per foot. There are however uncertainties associated with finding water even if drilling is undertaken. Further, if the drilling is successful, F would be able to use the water from the well for his own farming, and cannot sell it to others, as N is the dominant seller of water in the region. The water table in the region is too low, and F was sure not to hit the water table, before a depth of 200 feet. There is no guarantee that he would find water even if the drilling is done to a depth of 200 feet. Only 60 percent of the surrounding farms could find water at a depth of 200 feet. If F decides to drill deeper than 200 feet, F should commit to the drilling contractor to drill to a further depth of 50 feet (ie to a total depth of 250 feet). There was almost no chance of finding water below 250 foot depth. As per the data of wells in the surrounding region, digging beyond 200 feet resulted in finding water only in ten percent of the attempts, and the rest 90 percent were failures. What should F do? What is the expected value of perfect information for F