# At a small airport, an airline company is purchasing a new tractor to bring luggage to and from the airplanes. The tractor will be needed for only three years since a new mechanized luggage system wil

At a small airport, an airline company is purchasing a new tractor to bring luggage to and from the airplanes. The tractor will be needed for only three years since a new mechanized luggage system will be installed in three years. However, because the tractor will be used heavily, and maintenance costs are hight, it may still be economical to replace the tractor after 1 or 2 years with a brand-new one. The following table gives the total present value of the cost associated with buying a tractor in year i and trading it in year j (where year 0 is now): 0 8 18 31 110 21 2 12 The problem is to determine at what times the tractor should be replaced (if ever) to minimize the total cost for tractors. (a) [3 points] Draw the corresponding shortest path network graph, showing and explaining the nodes, arcs, and any relevant parameters. (b) [7 points] Formulate this problem as a shortest path problem.

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