Shamrock Oil $($see Problem $8-37)$ has decided to rely on utility theory to assist in the decision

concerning the oil field. The following table describes its utility function; all monetary values are in

thousands of dollars:

$($a$)$ Redo Problem $8-37$ using this information.

$($b$)$ How can you best describe Shamrock Oil's attitude toward risk? Justify your answer.

References see Problem $8-37$

Shamrock Oil owns a parcel of land that has the potential to be an underground oil field. It will

cost $$500,000$ to drill for oil. If oil does exist on the land, Shamrock will realize a payoff of

$$4,000,000($not including drilling costs$).$ With current information, Shamrock estimates that there

is a $0\mathrm{.}2$ probability that oil is present on the site. Shamrock also has the option of selling the land

as is for $$400,000,$ without further information about the likelinood of oil being present. A third

option is to perform geological tests at the site, which would cost $$100,000.$ There is a $30\%$

chance that the test results will be positive, after which Shamrock can sell the land for $$650,000$

or drill the land, with a $0\mathrm{.}65$ probability that oil exists. If the test results are negative, Shamrock

can sell the land for $$50,000$ or drill the land, with a $0\mathrm{.}05$ probability that oil exists. Using a

decision tree, recommend a course of action for Shamrock Oil.