PROBLEM 1 On a peaceful neighborhood in Calgary live two types of people: those who like buying a Regular amount of toilet paper, and those who like buying a Massive amount of toilet paper. On any given day, any of the many stores in the neighborhood can be visited by two random individuals looking to buy toilet paper. How much toilet paperthey can get depends on their types: a If the two individuals like buying a Regutor amount, both will be able to buy the amount they need, so both will get an enjoyment level of 12. I If the individuals are of different type, the one who likes buying a Massive amount will hog all the toilet paper, getting an enjoyment level of 10, while the one who likes buying Regular amounts will go home with nothing, and will get an enjoyment level of U. I If the two individuals like buying a Massive amount, both will obtain only a fraction of the amount they*re looking for, meaning both will receive an enjoyment level of only 6. Part 1 {5 marks]. Build a payoff matrix to summarize this problem. Part 2 {5 marks}. Let r represent the proportion of individuals who like buying a Regular amount of toilet paper. Write, in terms of r, the fitness functions of each type of individual in the neighborhood. Part 3 {5 marks). Graph the fitness functions you found in the previous question. The axis of your graph and the lines you draw in it must be properly labeled. lfthey intersect make sure to indicate the value of r and the fitness level at which this happens. Part 4 [5 marks]. indicate, with arrows on the horizontal axis of your graph, the evolutionary trends for 2'". Part 5 {5 marks]. TRUE or FALSE: This system has a stable polymorphic equilibrium. Explain. Part E [5 marks). Suppose that the population living in this neighborhood was originally at one of the equilibria that has 1' :- i], but one day a natural catastrophe occurred. A consequence of this catastrophe was that buyers of Massive amounts oftoilet paper living in otherr parts of Calgary decided suddenly to start visiting the peaceful neighborhood every day in search of emergency toilet paper to assuage theirfears. Because ofthis, the proportion of Regular toilet paper buyers dropped by 30 percentage points. Describe how the population living on this neighborhood evolved after this sudden drop