4. Paola, Qingmin, Rhonda, Santeri, and Truc live on the same street. They are considering jointly spending money to plant some trees to beautify their street. Trees are a public good, i.e. each tree benefits everyone, but different people enjoy trees to different degrees. Each of the five neighbors is able to quantify their enjoyment from the trees in dollar terms (i.e. they have quasi-linear utility). If z > 0 trees are planted then: e Paola gets 800,/z dollars worth of benefit from the trees; e Qingmin gets 600/ dollars of benefit; e Rhonda gets 200./z dollars of benefit; e Santeri gets 4004/x dollars of benefit; e Truc gets 360+/z dollars of benefit. Each tree that is planted costs 100 dollars. The neighbors have agreed that the costs will just be divided equallyso everyone pays 20 dollars per tree. So the only question is how many trees to plant. Since everyone has different preferences about this, and they need to make a decision jointly, they plan to vote. Specifically, they would like to use Condorcet's voting method. Suppose that the group of neighbors can choose any number of treesx = 1,2, ..., 500. (The street is not big enough to plant more than 500 trees.) Among these 500 al- ternatives, is there a Condorcet winner? Explain. (Note: this is slightly different from the setting in class because people may be indifferent between some alternatives. This isn't a big deal for the problem; feel free to make any reasonable assumptions about tie-breaking if needed.)