The objective function (1) implies that all variable production costs as well as the transportation costs should be minimized. According to the constraints (2) each customer's demand for each product will be satisfied. Constraints (3) specify that for each type of product and for each plant the amount of the product shipped from the plant to all the customers cannot be greater than the quantity produced in that plant. Because of the inequality sign in constraints (4) the producers are not forced to operate in the whole planning period. Constraints (5) and (6) are nonnegativity constraints on all the variables.