SOLUTION!!!!!!
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.
- Please Only Nice Handwriting And I Want To See Step By Step Solution The Goferbroke Company Owns A Tract Of Land T 1 (20.11 KiB) Viewed 256 times
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.)
f) Calculate the expected value of perfect information (EVPI).
According to the result, determine if to proceed with the seismic
survey is worthwhile. (16 p.)
g) Calculate the expected value of experimentation (EVE). According
to the result, determine if to proceed with the seismic survey is
worthwhile. (20 p.)
TABLE 1 Prospective profits for the Goferbroke Company Status of Land Alternative oll Drill foro $712,880 Sell the land $127,300 Chance of status 3 in 10 Payoff Dry - $152,760 $127,300 7 in 10