Q$4)(15$ pts$)$ Consider the following graph Where $S$ is the start state and $G$ is the goal state.

Arcs show the edge costs. Assume that $A^{**}$ algorithm is applied using two different heuristic

values $H1$ and $H2.$

a$)(10$ pts$)$ Arrange the heuristic values so that both will be admissible$/$consistent and $H2$

will dominate $H1.$ Heuristic value for $G$ is $0$ in both cases.

b$)(5$ pts$)$ In general, if $HI$ and $H2$ are both admissible, which of the following

composition is better to use. Explain your reason.

i$)$ Max$(H1,H2)$

$($ii$)\frac{H1+H2}{2}$

$($iii$)$ Min$(H1,H2)$