Hello can you please help with this DFA exercise thank you

3. Consider modeling the problem of a farmer that has to transport a Goat, a Wolf and Cabbage in a boat across the river. Initially (start state), the farmer is on the left bank of the river. Furthermore, the boat can carry the farmer and only one of the other three. The farmer and his entire entourage has to cross to the right bank of the river. Note that the farmer can ferry each of the three but one at a time. However, if the farmer leaves the goat and the wolf unattended on either side of the river, the wolf will eat the goat. If the farmer leaves the goat and the cabbage unattended on either side of the river, the goat will eat the cabbage. Your task is to model this problem as a DFA and then determine a safe set of "moves that will transport all four across the river. A "safe" state is one where the items on the same side of the river are safe from being eaten by another item (i.e, cabbage is not eaten by the goat and the goat is not eaten by the wolf). A "move , and a "move is a transition labeled by either F, G, C, W where F denotes the farmer alone crosses the river, G denotes that the farmer and goat cross the river, W denotes that the farmer and wolf cross the river, and C denotes farmer and cabbage cross the river. Below are some hints to get you started with modeling this problem using a DFA: the start state has all four on left bank of the river and none (empty set) on the right bank of the river. each transition will end up changing the contents on the left bank and right bank (for example, a transition labelled C from start state will lead to a state that denotes Wolf and Goat on left bank and Farmer and Cabbage on the right bank). Note that the farmer can cross the river alone The farmer can cross from left to right bank or from right to left bank (with or without other items). The final state, that denotes a safe transportation of all the items, will have all four on the right bank of the river. To simplify the transition graph for the DFA, you can look at deriving the transitions that lead from one safe state to another