The process of modeling using linear programming is fairly consistent: define the decision variables, objective, and constraints.
Decision Variables. In this case, the decision variables are the number of units of each outlet to purchase. Let be the number of TV spots, and the number of magazine pages.
Objective. Our objective is to minimize the amount we spend: .
Constraints. We have one constraint for each market segment: we must be certain that we reach sufficient people of each segment. For boys, this corresponds to the constraint:
Similar constraints for the other segments gives us the full formulation as: