A delivery truck must plan a tour that visits $5$ customers, leaving node $0$ and returning to node $0$ at the end of the tour. The distance between each pair of nodes is given in the table below. $1.$ Find the tour and total distance using the nearest neighbor algorithm.

$2.$ Can you improve on the tour found in the previous point? What procedure did you follow to find a better solution?

$3.$ If the truck had a limited load capacity, what would you do differently in your previous procedure?

$4.$ Under what conditions do you not recommend using the closest algorithm to find the solution to implement? $\backslash$table$[[,0,1,2,3,4,5],[0,-,17,18,7,25,6],[1,17,-,28,15,16,19],[2,18,28,-,26,19,27],[3,7,15,26,-,20,14],[4,25,16,19,20,-,19],[5,6,19,27,14,19,-]]$