Drilling decisions by oil and gas operators involve intensive capital expenditures made in an environment characterized by limited information and high risk. A well site is dry, wet, or gushing. Historically, 50% of all wells have been dry, 30% wet, and 20% gushing. The value (net of drilling costs) for each type of well is as follows: Wildcat operators often investigate oil prospects in areas where deposits are thought to exist by making geological and geophysical examinations of the area before obtaining a lease and drilling permit. This often includes recording shock waves from detonations by a seismograph and using a magnetometer to measure the intensity of the Earth’s magnetic effect to detect rock formations below the surface. The cost of doing such studies is approximately $15,000. Of course, one may choose to drill in a location based on “gut feel” and avoid the cost of the study. The geological and geophysical examination classify an area into one of three categories: no structure (NS), which is a bad sign; open structure (OS), which is an “OK” sign; and closed structure (CS), which is hopeful. Historically, 40% of the tests have resulted in NS, 35% resulted in OS, and 25% resulted in CS readings. After the result of the test is known, the company may decide not to drill. The following table shows probabilities that the well will actually be dry, wet, or gushing based on the classification provided by the examination (in essence, the examination cannot accurately predict the actual event): a. Construct a decision tree of this problem that includes the decision of whether or not to perform the geological tests. b. What is the optimal decision under expected value when no experimentation is conducted? c. Find the overall optimal strategy by rolling back the tree.