Even though independent gasoline stations have been having a difficult$$ time, Ian Langella has been thinking about starting his own independent gasoline station. $$ Ian's problem is to decide how large his station should be$.$ The annual returns will depend on both the size of his station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful$$ analysis, Ian developed the following$$ table:

States of Nature

Size of First Station

Good Market

Fair Market

Poor Market

Small

$ $50$ comma $000$

$ $20$ comma $000$

negative $ $10$ comma $000$

Medium

$ $80$ comma $000$

$ $30$ comma $000$

negative $ $20$ comma $000$

Large

$ $100$ comma $000$

$ $30$ comma $000$

negative $ $40$ comma $000$

Very Large

$ $300$ comma $000$

$ $25$ comma $000$

negative $ $160$ comma $000$

For$$ example, if Ian constructs a small station and the market is$$ good, he will realize a profit of $ $50$ comma $000.$

This exercise contains only part e$.$

Part $2$

$$e$)$ The correct decision tree for$$ Ian, if each outcome is equally$$ likely, is presented in

$$

$.$