In planning farm operations for the current year, a farmer can choose from two crops, A and B. The profits (in dollars) of the crops depend on the amount of rainfall according to the following table.

Rainfall CROP A CROP B

Heavy $7,500 $3,000

Moderate $3,500 $3,000

Light $1,500 $5,000

The farmer estimates the chance of heavy rainfall to be 20%, moderate rainfall 35%, and light rainfall as 45%. What crop should the farmer plant? why or why not?

Show all your work. Explain your answer using the relevant equations. Your explanation determines your grade