Monkey and Bananas problem

One of the standard AI toy search problems is the monkey and bananas problem. The variation of this problem that we will use is: A monkey is in a room containing a bunch of bananas and a wooden box. The bananas are hanging from the ceiling out of the monkeys reach, but he can reach them if he stands on the box. Unfortunately (for the monkey) the monkey, box, and bananas are all in different places in the room. What does the monkey have to do to get the bananas?

1. Formalize this problem using a state space representation, designed for a forward search (initial to goal states). A state space representation formalizes a problem in terms of the following elements:

1. a description of how states will be represented and what legal states are;

2. a description of the initial state(s);

3. a description of the goal state(s); and

4. a description of the legal operators, showing what states they can be applied in and what the resulting state is.

5. A description of the sensors that the monkey has. Describe the relationship between checking the sensors and making a move. (Hint: Think about the state space representation for the vacuum world problem.)