Question $1$

Ms$.$ Ulsan has been thinking about starting her own independent gasoline station. Ms$.$ Ulsan's problem is to decide how large her station should be$.$ The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline. The probabilities of a good market : fair market : poor market are $0\mathrm{.}5$:$0\mathrm{.}3$:$0\mathrm{.}2.$ Suppose an industry expert might provide a prediction service on industry and market performance, and so clients will know, before arriving at the decision, what the actual market stage would be$.$ After a careful analysis, Ms$.$ U $$ an developed the following payoff table

$\backslash$table$[[$Size$/$ Market condition,Good,Fair,Poor$],[$Small$,50,000,20,000,-10,000],[$Medium$,80,000,30,000,-20,000],[$Large$,100,000,35,000,-40,000],[$Very Large,$300,000,45,000,-160,000]]$

What decision would Ulsan make if she were extremely optimistic$/$extremely pessimistic$/$risk neutral about the future scene? Suppose Ulsan has no idea about the likelihood of the future scene.

If the prediction is $100\%$ accurate, what is the maximum amount should Ulsan pay for this piece of advice?

What decision would Ulsan make if she wants to minimize her maximum regret and expected regret?