Miles is considering buying a new pickup truck for his lawn service firm. The economy in town seems to be growing, and he is wondering whether he should opt for a subcompact, compact, or full-size pickup truck. The smaller truck would have better fuel economy, but would sacrifice capacity and some durability. A friend at the Bureau of Economic Research told him that there is a 30% chance of lower gas prices in his area this year, a 20% chance of higher gas prices, and a 50% chance that gas prices will stay roughly unchanged. Based on this information, Miles has developed a decision table that indicates the profit amount he would end up with after a year for each combination of truck and gas prices. Develop a decision tree for this situation and indicate which type of truck he should select.

\begin{array} { | l | c | c | c | } \hline & { \text { States of Nature } } \\\hline \text { Alternatives } & \text { Lower gas prices } & \text { Gas prices unchanged } & \text { Higher gas prices } \\\hline \text { probability } & .3 & .5 & .2 \\\hline \text { Subcompact } & 16,000 & 19,000 & 21,000 \\\hline \text { Compact } & 15,000 & 20,000 & 22,000 \\\hline \text { Full size } & 24,000 & 19,000 & 6,000 \\\hline\end{array}

The Expected Value with Perfect Information

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