3. (10 marks) Consider the following scenario. Due to population growth, a shift in demographics and a push to have children walk to school to increase fitness, the city of Toronto needs to rezone it's schools some schools currently have too many students and some not enough, some are just too far away That is, for each school the catchment area needs to be adjusted so that children in the neighbourhoods are assigned to schools within lkm of their home while ensuring that schools are not overloaded with too many students. Suppose that the census has identified that there are n children in Toronto and k schools. Each of the n children needs to be assigned to a school such that no school has more than 1 students and the child Give a polynomial-time algorithm that given the distances for each child from all schools, determines whether it is possible to assign each child to a school. Hint: Set up a network flow... s home is within lkm of their school 3. (10 marks) Consider the following scenario. Due to population growth, a shift in demographics and a push to have children walk to school to increase fitness, the city of Toronto needs to rezone it's schools some schools currently have too many students and some not enough, some are just too far away That is, for each school the catchment area needs to be adjusted so that children in the neighbourhoods are assigned to schools within lkm of their home while ensuring that schools are not overloaded with too many students. Suppose that the census has identified that there are n children in Toronto and k schools. Each of the n children needs to be assigned to a school such that no school has more than 1 students and the child Give a polynomial-time algorithm that given the distances for each child from all schools, determines whether it is possible to assign each child to a school. Hint: Set up a network flow... s home is within lkm of their school