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Q3: A robot R is located at the bottom left corner in a 2-dimensional maze that is made up of 4-by-4 (i.e. total of 16) grid locations as visualized by Table 1. The robot R can move in 4 directions (i.e., up, down, left, right) within the grid, and must end up in the goal location G in at most 9 moves. A block B represents a type of location that the robot R cannot move to or from. The numbers on the grid locations represent the one-time reward Q that can be collected by the robot R by moving to the respective location. 1G 2 BB1 2 1 2 R Table 1: Visualization of the maze for Q1. a: For 23 marks, formulate a DP model such that the robot R navigates the maze and reaches the goal location with maximum total reward Q. Clearly present your assumptions, stages, states, decision variables, transition relation, immediate return and cumulative return. b: For 10 marks, solve the DP