Discus the below:
Often in optimization modeling, there is some interaction between two decisions. For example, if we open two warehouses in our fixed-charge minimum cost network flow model, there could be a savings involved due to their proximity. This can be modeled in the objective function using the nonlinear term Cx_i x_j, where x_i, x_j are both 0 - 1 (binary) variables. Since we cannot handle nonlinear terms using what we know, we wish to model this using linear terms and constraints. One method is to create a new variable y_ij and constrain it somehow to satisfy the equation y_ij = x_i x_j when all variables are integers. What constraints would you use to guarantee this relationship?