The Parks Department has $10 million in this year's budget to spend on the renovation of small community parks. Although there are hundreds of these parks, only a few can be fixed each year. The Parks Department has two programmatic approaches to such improvements. The first is a complete rebuild of a small park from the ground up, and the second is a partial fix-up such as the replacement of the children's play equipment, resurfacing the basketball courts, or replacing the trees and bushes. A complete rebuild costs about $1 million and takes 18 months to finish. The partial fix-ups cost about $500,000 and take 6 months to finish. The Department estimates that more long-term community benefit is created from a complete rebuild than from a partial fix-up. Surveys of citizens living near parks that have had similar renovations bear out this belief. In fact those surveys indicate that the public receives two and one- half times the long-term benefit from the complete rebuild than from the partial fix-up. (2.5"bennys" for a rebuild and 1 "benny" for a fix-up.) Since the Department must report to the City Council the parks it repairs, the Department believes it must repair at least one park in each of New York's five Borough. To guarantee that at least one of either type is done in each Borough, it must plan to do a total of at least five. If the Department fixes less than five, then a Borough will be left out. If it does five or more, all Boroughs will have at least one, which is acceptable. (For example three complete rebuilds plus 2 partial fix-ups would be sufficient for this requirement.) However since the community does not have use of the park during renovation, there is a short-term community loss during construction. The Mayor's advisors, based on a combination of research and intuition, believe that this short-term community loss can cost votes if the total collective amount of out of service time for parks gets too high. They want the Parks Department to limit the sum total number of months all parks being renovated under these two programs are out of service to no more than 150 months. (i.e. if you do 2 rebuilds and 3 fix-ups the total time out of service is 2 times 18 plus 3 times 6 for a total of 54 months.) The Parks Departments therefore wants to get the most long-term community benefit (maximize total bennys) for its $10 million (that's all it has, not a penny more) without getting the Mayor's advisors or the City Council upset. 1) Find the mix of complete rebuilds and partial fix-ups that satisfies all these concerns. (i.e. formulate write out - a Decision Model and use graphical analysis to find the best feasible combination of the two types of renovations. For this problem your answers do not have to be whole numbers. You may fix 1.5 parks.) 2) After you have found that answer, what would be your answer if it was determined that the partial fix-ups provided only 0.9 bennys? Would your answer change? 3) What would your answer be if there was no need to do one park per borough (eliminated the constraint)? Would your answer change
