For a given school district the following is known. There are G grades and J schools. Each school j has a capacity C_jg for grade g. In each of I neighborhoods in the district, there is a student population S_ig for neighborhood i and grade g. Let the distance from neighborhood i to school j be represented by d_ij. All of these are the parameters that the school distinct has to take as a given. Note that none of these are decision variables. Formulate a model to assign all students to schools without violating the capacity each school has for each grade while minimizing the total distance traveled by all students. In your formulation you can ignore the fact that the number of students must be an integer. Now let S_ikg = the number of students in neighborhood i of race k and grade g; a_k = the maximum percent of racial group k assigned to any school; and b_k = the minimum percent of racial group k. Reformulate the model while also satisfying the racial-balance constraints.