Farmer McCoy can plant either corn or soybeans. The probabilities that the next harvest prices will go up$,$ stay the same, or go down are $\mathrm{.}25,\mathrm{.}30,$ and $\mathrm{.}45,$ respectively. If the prices go up$,$ the corn crop will net $$30,000$ and the soybeans will net $$10,000.$ If the prices remain unchanged, McCoy will $($barely$)$ break even. But if the prices go down, the corn and soybeans crops will sustain losses of $$35,000$ and $$5000,$ respectively.

$($a$)$ Represent McCoy$$s problem as a decision tree.

$($b$)$ Which crop should McCoy plant?

Please Explain, calculate and find answer detailly step by step because I want to understand how calculate this type of exercises. And please don$$t put answers of other experts which answered this question before I asked you.