This is the case also for the S U M operator in the maximum inventory constraints. By contrast, the left-hand side of the maximum sales constraints is just a single decision variable for each of the 1,000 combinations of a plant, product, and month. (Separating these upper-bound constraints on individual variables from the regular functional constraints is advantageous because of the computational efficiencies that can be obtained by using the upper bound technique described in Sec. 7.3.) No lower-bound constraints are shown here because MPL automatically assumes that all 21,000 decision variables have non negativity constraints unless nonzero lower bounds are specified. For each of the 3,100 functional constraints, note that the left-hand side is a linear function of the decision variables and the right-hand side is a constant taken from the appropriate data file. Since the objective function also is a linear function of the decision variables, this model is a legitimate linear programming model.