Problem $4$

Even though independent gasoline stations have been having a difficult time in recently years, Susan

Solomon is thinking about starting her own independent gasoline station. Before starting construction,

Susan needs to determine the size of her gasoline station since the annual return will depend on both the

size of her station and a number of marketing factors related to the oil industry and demand for gasoline.

After some careful calculations, Susan developed the following table.

Which alternative $($size of the gasoline station$)$ should Susan choose if the decision criterion is:

A maximax?

B maximin?

C equally likely?

D minimax regret?

After some discussion with her friends in oil industry, Susan estimates $($subjectively$)$ that the

probabilities of having a good market, fair market, and poor market are $0\mathrm{.}3,0\mathrm{.}4,$ and $0\mathrm{.}3,$

respectively.

A$.$ Determine the expected profit $($EMV$)$ for each decision alternative. Which alternative is the

best?

B$.$ Compute the expected value of perfect information $($EVPI$).$

Problem $5$

For the above problem, Susan would like to consider the option of hiring a consulting company

before making her final decision. The consulting company offers to do some market research for

the future gasoline market at the cost of $$7500.$ Since the consulting company has done similar

research before, it tells Susan that the research will be either positive or negative and historically

the research is positive $85\%,45\%,$ and $20\%$ of the time when the future market demand is good, fair,

and poor, respectively. So now Susan has two decisions to make: $1)$ whether to hire the consulting

company to have the market research done, and $2)$ the original capacity problem, i$.$e$.,$ whether to

start a small, medium, or large size gasoline station.

Draw a decision tree taking into account both decisions that need to be made. Make sure to

include all probabilities for the states of nature, and the EMV's for each node

What should Susan do$?($write down the course of action and expected payoff$)$

Assuming the decision is made to do the market research, what should be the fair value of the

market research by the consulting company? $($Hint: the fair value of the market research is the

value at which Susan is indifferent between choosing the research option and not choosing it$)$