4. 130 pts) Some oil company owns a tract of land that may contain oil. There are four possible types of the land: producing 500,000 barrels (S), producing 200,000 barrels (Sa), producing 50,000 barrels (Sa), or no oil (S). According to the experience, the probabilities of the land belonging to the above four types are 0.15, 0.15,0.2,0.3 respee- tively. Now, the company has three options: holding the land in onder to drill for oill itself, reating the land to another oil company without any condition, or renting the land The cost of drilling the land is $100,000 with oil or $70,000 without oil, and the revenue of oil is $2 per barrel. If the company rents the land unconditionally, it will receive $45,000 If the company rests the land conditionally, when the production of oil is between 200.000 and 500,000 barrels, the company will receive $0.3 per barrel. (a) Develop a decision analysis formmlation of this problem by identifying the decision alternatives, the state of nature, and the payolf table (b) Develop a probability tree diagram to obtain the posterior probabilities of the rut of the test Now, the company decides to conduct a detailed seismic souading survey of the land to obtain a better estimate of the probability of oil, which costs the company $10.000 The possible results of the survey are: Excellent seismic soundings (), good seismic soundings (a). fair seisunic soundings (Ja), or poor seismic soundings (). Based on past experience, the probabilities are given as 1 058 0.33 0.09 0.00 2056 0.19 0.125 0125 0.49 026 0125 0.125 S0.19 027 031 0.23 (c) Find EVPI for this problem (d) Find EVE for this problem. (e) Develop a decision tree diagram Should the company conduct the survey? Interpret your selection What would be the optimal decision 4. 130 pts) Some oil company owns a tract of land that may contain oil. There are four possible types of the land: producing 500,000 barrels (S), producing 200,000 barrels (Sa), producing 50,000 barrels (Sa), or no oil (S). According to the experience, the probabilities of the land belonging to the above four types are 0.15, 0.15,0.2,0.3 respee- tively. Now, the company has three options: holding the land in onder to drill for oill itself, reating the land to another oil company without any condition, or renting the land The cost of drilling the land is $100,000 with oil or $70,000 without oil, and the revenue of oil is $2 per barrel. If the company rents the land unconditionally, it will receive $45,000 If the company rests the land conditionally, when the production of oil is between 200.000 and 500,000 barrels, the company will receive $0.3 per barrel. (a) Develop a decision analysis formmlation of this problem by identifying the decision alternatives, the state of nature, and the payolf table (b) Develop a probability tree diagram to obtain the posterior probabilities of the rut of the test Now, the company decides to conduct a detailed seismic souading survey of the land to obtain a better estimate of the probability of oil, which costs the company $10.000 The possible results of the survey are: Excellent seismic soundings (), good seismic soundings (a). fair seisunic soundings (Ja), or poor seismic soundings (). Based on past experience, the probabilities are given as 1 058 0.33 0.09 0.00 2056 0.19 0.125 0125 0.49 026 0125 0.125 S0.19 027 031 0.23 (c) Find EVPI for this problem (d) Find EVE for this problem. (e) Develop a decision tree diagram Should the company conduct the survey? Interpret your selection What would be the optimal decision