2. Consider the following problem: You have three jugs with capacities 4, 5 and 6 litters respectively. Initially all of the jugs contain 2 litters of water. At any time-step, you can either remove 1 litter of water from any 2 jugs or add 1 litter to any 1 jug. You have to continue the process until the jugs contain 8 or more litters of water in total. The target is to reach the goal within minimum number of steps. Answer the following: a. How many variables are required to mathematically represent the states of the problem? b. What is the size of the state-space? Explain your calculation. c. List any 30 goal states. d. Will a DFS find optimal solution for this problem? What about a BFS? Which one would you go for, and why?

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