(Solved) : 18 27 20 21 17 18 18 20 14 20 18 24 17 17 31 35 Q33127021 . . .
![5. In the maximum covering problem, we assumed that faiities cost the same amount to build. We also did not worry about the demands that could not be covered. Often, these are not good assumptions. First, in many cases, it makes sense to consider a model in which we minimize the sum of the construction costs, and a penalty cost for not covering demands in the desired time, To. Assume that the costs and penalties (f and p) are defined in commensurable terms. Second, we may require that all demands be covered within a time t1, where T>T Formulate such a model using the following Inputs 1=Set of demand nodes J- set of candidate locations To- desired coverage time (demands not covered within this time will be penalized in the objective function) T1- required coverage time (T1>T and all demands must be covered by at least one facility within time T) ti-travel time from demand node ie l to candidate site jeJ h:demand at node ie I fixed cost of locating a facility ant nodeje pi: penalty cost per unit demand not covered at demand node ie l o 1 tSTO ilo if not ij ijlo if not Decision Variables: 1 if a facility is located at candidate site je] if not 1 if demand node iel is covered by at least one facility within ime T if not Formulate the following problem MINIMIZE Total facility costs+ penalty costs SUBJECT TO Relationship between coverage within To and location decisions All demands covered within T1 Integrality](https://media.cheggcdn.com/media%2Fecf%2Fecf3fb68-83c7-4572-b81c-7612be40029d%2Fimage.png)
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