Develop a model to provide the smallest number of locations, but make sure that each zone is covered by at least two boxes.
Your express package courier company is drawing up new zones for the location of drop boxes for customers. The city has been divided into seven zones. You have targeted six possible locations for drop boxes. The list of the seven zones and which drop boxes could be reached easily from each zone is listed below.
Let xi = 1 if drop box location i is used, 0 otherwise
Min ?xi
s.t. x1 + x2 + x5 + x6 ? 2
x2 + x4 + x5 ? 2
x1 + x2 + x4 + x6 ? 2
x3 + x4 + x5 ? 2
x1 + x 2 + x5 ? 2
x3 + x4 ? 2
x1 + x2 + x6 ? 2
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