Linear programming
Just need constraint for "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 the seven zones shown below. You have targeted six possible locations for drop boxes. The list of which drop boxes could be reached easily from each zone is listed below.
Zone Can Be Served By Locations:
Downtown Financial 1, 2, 5, 6
Downtown Legal 2, 4, 5
Retail South 1, 2, 4, 6
Retail East 3, 4, 5
Manufacturing North 1, 2, 5
Manufacturing East 3, 4
Corporate West 1, 2, 6
Let xi = 1 if drop box location i is used, 0 otherwise.
Formulate a model to provide the smallest number of locations yet make sure that each zone is covered by at least two boxes. Then solve and report answers in spaces provided.
Formulation: (define variables, give objective function, give all constraints):