Remember the homework question from last week where we consider a school district with I={1,,I} neighborhoods, J={1,,J} schools and G={1,,G} grades at each school. Each school jJ has capacity Cjg for grade gG. In each neighborhood iI, the student population of grade gG is Sig. Finally, the distance from neighborhood iI to school jJ is dij. Last time the question was to formulate a linear integer programming problem to assign all students to schools, while minimizing the total distance traveled by all students. Now we add a twist and reformulate this problem with additional requirements. (a) Now assume that all students going to the same grade in a neighborhood have to be assigned to the same school. Formulate an integer program and explain your variables, constraints and objective function clearly. (b) Now assume that all students from the same neighborhood have to go to the same school. Formulate an integer program and explain your variables, constraints and objective function clearly