A farmer needs to move a hen, a fox, and a bushel of grain from the left side of the river to the

right using a raft. The farmer can take one item at a time (hen, fox, or bushel of grain) using

the raft. The hen cannot be left alone with the grain, or it will eat the grain. The fox cannot

be left alone with the hex, or it will eat the hen. For example, the farmer cannot move from

one side x of the river to the other side y if it would mean leaving the fox and hen together

on side x.

The farmer can load an item onto the raft, move the raft from one side of the river to the

other, or unload an item from the raft. The farmer wants to move the items with the fewest

number of trips across the river as possible, but does not care about how much time is spent

loading or unloading.

(a) Classify this problem using the primary representational dimensions.

(b) Represent this problem as a graph search problem. Be sure to include and

formally describe each component of the search problem.

(c) What is the forward branching factor for your representation from part (2b)?

Justify your answer.

(d) Construct a non-constant admissible heuristic for this problem.

(e) Argue that the heuristic from part (2d) is admissible.