A residential moving company needs to move a family from city 1 to city 12 in the figure below where the numbers on the arcs represent the driving distance in miles between cities.

(a)

Create a spreadsheet model for this problem. What is the optimal solution? (Enter your answer as an ordered comma-separated list of the city numbers of the optimal path.)

(b)

Suppose the moving company gets paid by the mile and, as a result, wants to determine the longest path from city 1 to city 12. What is the optimal solution? (Enter your answer as an ordered comma-separated list of the city numbers of the optimal path.)

2 3 6 6 5 8 8 9 10 11 12 2 3 6 6 5 8 8 9 10 11 12