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# Exactly one piece of equipment

A simple replacement problem for one kind of equipment having a 3-year lifetime can be represented by the following network diagram: Each node represents a year in your planning horizon. An arc from node i to node j represents the possibility of buying equipment in year i and holding it until year j. Thus the decision variable corresponding to the arc is: xij pieces of equipment bought in year i, and used until year j The associated cost is: cij net cost of buying one piece of equipment in year i, operating and maintaining it through year j – 1, and selling it in year j In the example represented by the diagram, the costs are shown adjacent to the arcs; for example, c12 is 10, and c25 is 26. All of the following questions pertain to the example. Where part of a constraint is given, fill in the rest of it
(3 points) Exactly one piece of equipment is to be purchased in the first year. What is the linear constraint corresponding to this requirement?

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