Question: Problem 7 (20 Points; Adapted from Winston, 2004). The Smalltown Fire Department currently has seven conventional ladder companies and seven alarm boxes. The two closest

Problem 7 (20 Points; Adapted from Winston,

Problem 7 (20 Points; Adapted from Winston, 2004). The Smalltown Fire Department currently has seven conventional ladder companies and seven alarm boxes. The two closest ladder companies to each alarm box are given in the following table. Two Closest Alarm Box Ladder Companies 1,5 - 3,4 6, 7 1,6 2,5 2, 4 The city wants to maximize the number of conventional ladder companies that can be replaced with tower ladder companies. Unfortunately, political considerations dictate that a conventional company can be re- placed only if, after replacement, at least one of the two closest companies to each alarm box is still a conventional company. Part a (10 points): Formulate an ILP that can be used to maximize the number of conventional companies that can be replaced by tower companies

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