$6.$ Consider the wildcatter problem that was shown in class $($Unit $3)$

a$.$ Calculate the P$(\backslash$theta $1)$ for which the EMV of the two decisions become equivalent. Below this probability value, the EMV of alternative $\backslash$alpha $2,$ not to drill, would be larger, and therefore alternative $\backslash$alpha $2$ would be favored based on this information

b$.$ State whether the oil drilling company should make the decision between these two

alternatives based only on this information. State what other information could lower

uncertainty to help them make a better decision

c$.$ How could this decision depend on company size or resources? Consider this decision for two company sizes: a small company, where $$1\mathrm{.}5$ Million is a large fraction of their resources compared to a larger company with ten times the resources of the smaller company. Would a smaller company have a greater aversion to the risk than the larger company?

d$.$ If a test of the rock strata is performed and the probability of significant oil presence based on this information is increased to $0\mathrm{.}5,$ calculate the expected value of the alternative to drill. State whether this monetary value should $($or would likely not$)$ offset the nominal cost of obtaining the additional information for an optimum decision.

e$.$ If the test of the rock strata costs $$50,000($TC$),$ estimate the monetary value of information $($VI$)$ gained from the test, where VI $=($optimum value following the test$)($optimum value without the test$).$ To be cost effective, the VI should be significantly greater than the cost of the tes