1. Consider the network shown below, Link distances are shown besides the links and the demands in boxes beside each node. a) Use the greedy adding algorithm to solve the maximum covering problem for this network with a coverage distance of 34 and as single facility. Assume you can only locate on the nodes of the network. In particular, where do you locate? How many demand are covered? Which nodes are covered and which are not? 20 21 18 18 18 17 17 31 b) For a coverage distance of 34 use the greedy adding algorithm (without substitution) for the maximum covering problem to complete the following table. Number of facilities Facility locations Total Covered Covered Demand Note: You may not need all rows of the table. 2, a) For the network shown above, write out the set covering problem formulation for a coverage distance of 34 b) For the problem formulated in part (a), can you eliminate any columns (e.g. force out any nodes)? Can any nodes be forced in? Can any rows be eliminated? After forcing in and out any nodes that can be forced in this way and eliminating any rows, find an optimal solution to the problem c) What if anything does your solution tell you about the results you obtained in part (b) of Question 1? d) What if anything does your solution tell you about the objective function for the 3-center problem? e) What if anything does your solution tell you about the objective function for the 2-center