okay so i need help with the working part for point C-G and C-F. do i need to use G(ABCG), G(ABCF) OR G(ACG), G(ACF)? thanks for helpiing out.

Consider the following search problem, represented as a graph. Each node is label by a capital letter and the value of a heuristic function is shown in maroon. Each edge is labelled by the cost to traverse that edge. The start state is ' A ' and the only goal state is ' G '. Perform the A * search to find the shortest path from node A to node G. i. Is the heuristics specified in the problem (shown below) admissible? Justify your answer. If the heuristics is admissible, proceed to answer part (ii). If the heuristics is not admissible, correct it with a sensible value of your choice and proceed to answer part (ii). (10.0 marks) ii. Perform the A search to find the shortest path from the start state (S) to the goal state (G). (20.0 marks) Numbers in maroon are the heuristics for the respective nodes. Numbers in black are the weight (estimated costs.) From the table above, the heuristic for states BE and DE are not admissible. Hence, the heuristic for the problem above is not admissible. To ensure optimal solution for the node E needs to be changed. It can be change from H=16 to H=18 Optimal Table: ii) closeset{A},open{C,G,D,E,B}AB,f(B)=g(AB)th(A)=(0+3)+27=30BE,f(E)=g(ARE+h(E)(3+9)+18=30BD1f(BE)=g(ABD)+h(2)=(3+10)+20BCF(BC)=g(ABC)+h(C)==(3+2A)+3closesct{A,B}=33=30 open AC,f(C)=g(AC1+h(C)=10+271+3=30