Considering the environment:

The professor $(2,6)$ needs to reach the gold coin $(2,0)$

Passing through an empty square costs $1($reaching the goal also$)$

Passing through a Dal$$ mask costs $6$ units

Passing through his glasses reduces his accumulated cost by $3$ units

Design a dominant heuristic for this problem

Apply A$*$ search, avoid backtracking in both cases

Determine an admissible and dominant heuristic for this problem and justify.

Show the generated tree and indicate the solution found.