We have a 10x10 grid with the blue dot representing the player, green cells with different reward values, and red squares with different penalty values. The blue dot can move in four directions: North, South, East, West. When the blue dot reaches a reward or a penalty square, the game ends and the value of the square is the final score. Find the players optimal path in order to maximize its reward. Plot the resulting optimal path and display the value function for each cell. Try your algorithm for discount factors of 0.8 and 0.9 and compare the results.