Q$4$: $25$ pts$)$ Consider the edge weight matrix below for a complete graph. Determine an approximation to the minimum weight tour using the $($i$-10)$ Nearest neighbor heuristic $($ii$-10)$ Twice around the tree heuristic.

Also, show one attempt of reducing the tour weight using the $2-$change heuristic for the tour obtained with each of the two heuristics.

Show all the work as well as clearly indicate the tour and its weight before and after the attempt of using the $2-$change heuristic in each case.

$\backslash$table$[[,$V$1,$V$2,$V$3,$V$4,$V$5,$V$6],[$V$1,0,2,10,15,14,6],[$V$2,2,0,7,3,14,8$