Problem $7.$ A traveling salesman is tasked with visiting all cities from A to F $,$ aiming to complete the journey with the shortest possible tour. The table below presents the distance matrix, showing the distances between each pair of cities. Using this information, the salesman needs to determine the optimal route that minimizes the total travel distance while ensuring that each city is visited exactly once before returning to the starting point.

Q$1.$ Solve it using the nearest neighbor heuristic $($starting from node $\backslash ($ A $\backslash )).(5$pts$)$

Q$2.$ Solve it using the cheapest insertion heuristic. $(5$pts$)$