Fruit Trees: You have room for up to two fruit-bearing trees in your garden. The fruit trees that can grow in your garden are either apple, orange, or pear. The cost of maintenance is $100 for an apple tree, $70 for an orange tree, and $120 for a pear tree. Your food bill will be reduced by $130 for each apple tree you plant, by $145 for each pear tree you plant, and by $90 for each orange tree you plant. You care only about your total expenditure in making any planting decisions.
a. What is the set of possible actions and related outcomes?
b. What is the payoff of each action/outcome?
c. Draw the associated decision tree. What will a rational player choose?
d. Now imagine that the reduction in your food bill is half for the second tree of the same kind. (You like variety.) That is, the first apple tree still reduces your food bill by $130, but if you plant two apple trees your food bill will be reduced by $130 + $65 = $195, and similarly for pear and orange trees. What will a rational player choose now?