Consider the TSP problem presented in $11-4.$

$11-4.$ A baseball fan wishes to visit eight major league parks in $(1)$ Seattle, $(2)$ San Francisco, $(3)$ Los Angeles, $(4)$ Phoenix, $(5)$ Denver, $(6)$ Dallas, $(7)$ Chicago, and $(8)$ Tampa before returning home to Seattle. The fan will use air transportation between the diffelent cities. The matrix $||p_{ij}||$ below provides the price in dollars of one$-$way ticket between the $8$ cities.

$||p_{ij}||=([0,250,300,290,240,320,380,450],[250,0,190,220,230,300,310,390],[300,190,0,140,310,295,390,410],[290,220,140,0,200,275,285,350],[240,230,310,200,0,240,255,400],[320,300,295,275,240,0,260,370],[380,310,390,285,255,260,0,420],[450,390,410,350,400,370,420,0])$

a$.$ Find the lower bound on the optimal tour length using the assignment model. Include a printout of your Excel Solver Solution. $(3$ points$)$

b$.$ Solve using Branch & Bound $($B&B$).(3$ points$)$

c$.$ Solve using the nearest neighbor heuristic. Assume you start at Chicago, $(2$ points$)$ Apply the reversal heuristic to the nearest neighbor solution from part $($c$).(3$ points$)$