The GOFERBROKE COMPANY owns a tract of land that may contain oil. A consulting geologist has reported to management that she believes there is 3 chances in 10 of oil. Because of this prospect, another oil company has offered to purchase the land for $127,300. However, Goferbroke is considering holding the land in order to drill for oil itself. The cost of drilling is $152,760. If oil is found, the resulting expected revenue will be $865,640, so the company's expected profit (after deducting the cost of drilling) will be $712,880. A loss of $152,760 (the drilling cost) will be incurred if the land is dry (no oil). Table 1 summarizes these data. TABLE 1 Stats Alternative Ow Prospective profits for the Golerbroke Company of Land $712,880 $127 300 3 in 10 Pelt Dry $152,760 $127,300 7in10 Selte od Chaco However, before deciding whether to drill or sell, the company wants to be conducted a detailed seismic survey of the land to obtain a better estimate of the probability of finding oil. The survey cost is $40,000 A seismic survey obtains seismic soundings that indicate whether the geological structure is favorable to the presence of oil. We will divide the possible findings of the survey into the following two categories: USS: Unfavorable seismic soundings; oil is fairly unlikely. FSS: Favorable seismic soundings; oil is fairly likely. Based on past experience, if there is oil, then the probability of unfavorable seismic soundings is P(USS State = Oil)=0.35, P(USS State Oil) = 0.65, Similarly, if there is no oil (i.e., the true state of nature is Dry), then the probability of unfavorable seismic soundings is estimated to be P(USS State = Dry)=0.8, P(USS State =Dry)=0.2. By using the given data; a) Calculate the posterior probabilities P (State =Oil Finding = USS) and P (State = Dry Finding=USS), if the founding of the seismic survey is unfavorable seismic soundings (USS), by using Bayes' theorem. (10 p.) b) Calculate the posterior probabilities P (State = Oil Finding = FSS) and P (State = Dry | Finding = FSS), if the seismic survey gives favorable seismic soundings (FSS), by using Bayes' theorem. (10 p.) c) Draw the probability tree diagram for the full problem by showing all the probabilities leading to the calculation of each posterior probability of the state of nature given the finding of the seismic survey. (20 p.) d) Calculate the expected payoffs and determine the optimal action if finding is USS. (12 p.) e) Calculate the expected payoffs and determine the optimal action if finding is FSS. (12 p.) 1) Calculate the expected value of perfect information (EVP). According to the result, determine if to proceed with the seismic survey is worthwhile. (16 p.) 9) Calculate the expected value of experimentation (EVE). According to the result, determine if to proceed with the seismic survey is worthwhile. (20 p.) The GOFERBROKE COMPANY owns a tract of land that may contain oil. A consulting geologist has reported to management that she believes there is 3 chances in 10 of oil. Because of this prospect, another oil company has offered to purchase the land for $127,300. However, Goferbroke is considering holding the land in order to drill for oil itself. The cost of drilling is $152,760. If oil is found, the resulting expected revenue will be $865,640, so the company's expected profit (after deducting the cost of drilling) will be $712,880. A loss of $152,760 (the drilling cost) will be incurred if the land is dry (no oil). Table 1 summarizes these data. TABLE 1 Stats Alternative Ow Prospective profits for the Golerbroke Company of Land $712,880 $127 300 3 in 10 Pelt Dry $152,760 $127,300 7in10 Selte od Chaco However, before deciding whether to drill or sell, the company wants to be conducted a detailed seismic survey of the land to obtain a better estimate of the probability of finding oil. The survey cost is $40,000 A seismic survey obtains seismic soundings that indicate whether the geological structure is favorable to the presence of oil. We will divide the possible findings of the survey into the following two categories: USS: Unfavorable seismic soundings; oil is fairly unlikely. FSS: Favorable seismic soundings; oil is fairly likely. Based on past experience, if there is oil, then the probability of unfavorable seismic soundings is P(USS State = Oil)=0.35, P(USS State Oil) = 0.65, Similarly, if there is no oil (i.e., the true state of nature is Dry), then the probability of unfavorable seismic soundings is estimated to be P(USS State = Dry)=0.8, P(USS State =Dry)=0.2. By using the given data; a) Calculate the posterior probabilities P (State =Oil Finding = USS) and P (State = Dry Finding=USS), if the founding of the seismic survey is unfavorable seismic soundings (USS), by using Bayes' theorem. (10 p.) b) Calculate the posterior probabilities P (State = Oil Finding = FSS) and P (State = Dry | Finding = FSS), if the seismic survey gives favorable seismic soundings (FSS), by using Bayes' theorem. (10 p.) c) Draw the probability tree diagram for the full problem by showing all the probabilities leading to the calculation of each posterior probability of the state of nature given the finding of the seismic survey. (20 p.) d) Calculate the expected payoffs and determine the optimal action if finding is USS. (12 p.) e) Calculate the expected payoffs and determine the optimal action if finding is FSS. (12 p.) 1) Calculate the expected value of perfect information (EVP). According to the result, determine if to proceed with the seismic survey is worthwhile. (16 p.) 9) Calculate the expected value of experimentation (EVE). According to the result, determine if to proceed with the seismic survey is worthwhile. (20 p.)
