Consider the problem of finding a path from city 1 to city 10 , using the heuristic given below in the ollowing table. 1. (1 pts) Draw the graph connecting the cities indicating the cost of each arc and the heuristic of each city mode. 2. (3 pts) Use the Best First search algorithm to find a path. Show the details of exploration of the algorithm. 3. (1 pts) What is the cost of path (from city 1 to the goal city) found by the algorithm (1 Mark) 4. (4 pts) Apply the A on the same problem. Show the details of exploration of the algorithm. (3 Marks) 5. (3 pts) Is the solution found by the A optimal? Justify and explain