Question $1.$ Construct a small undirected graph $($choose your own start and goal and connectivity$)$ and design the cost

for each node $($or edge, up to you$)$ on the graph. All costs need to be positive. Design a heuristic function $h$ such that

satisfies the following conditions

$h$ itself is consistent $($and of course, non$-$negative$).$

By multiplying it by $2($i$.$e$.$ the new heuristic function becomes $h^{\text{'}}(s)=2h(s)$ for each node $s),$ the new heuristic

is inconsistent and misguides $A^{**}$ search, such that it no longer returns the optimal path in the end.

Explain the computation steps of $A^{**}$ in each case to explain how the second heuristic value misguides the search.