In Part (a) you will draw a network to represent the problem. The nodes of the network represent time moments (when we may make decisions), as follows: Node 0 can be "now" (equivalently, the beginning of year 1), node 1 can be the end of year 1, node 2 the end of year 2 and node 3 the end of year 3. Nodes are connected with directed arcs (i,j), where i represents the time we purchase a tractor and j the time we trade it in with a new tractor, unless it is the end of year 3 and we do nothing. The attribute of each arc is the associated cost (that plays the role of distance). For example, there should be an arc from node 0 to node 1 at a cost of 8 (units in $1000), an arc from node 2 to node 3 at a cost of 12, an arc from node 1 to node 3 at a cost of 21, and so on... The path from node 0 to node 3 with the minimum cost is associated with the best replacement decisions during this 3-year time horizon

10.3-3. At a small but growing airport, the local airline company is purchasing a new tractor for a tractor-trailer train to bring luggage to and from the airplanes. A new mechanized luggage system will be installed in 3 years, so the tractor will not be needed after that. However, because it will receive heavy use, so that the running and maintenance costs will increase rapidly as the tractor ages, it may still be Page 415 more economical to replace the tractor after 1 or 2 years. The following table gives the total net discounted cost associated with purchasing a tractor (purchase price minus trade-in allowance, plus running and maintenance costs) at the end of year i and trading it in at the end of year ;(where year 0 is now). 1 2 0 2 $8,000 $18,000 $31,000 10,000 21,000 12,000 The problem is to determine at what times (if any) the tractor should be replaced to minimize the total cost for the tractors over 3 years. (a) Formulate this problem as a shortest-path