In this paper we consider a certain aggregate production planning model. This model permits regular and overtime production and allows for backordering of goods for a number of periods. Although the discussed model can be formulated as a linear programming problem a special (noniterative) method is developed. First the optimal level of each mode of production is determined for each period. Then the complete solution is immediately constructed. This procedure is so simple that it can be also implemented via pencil and paper. Several computational improvements as well as problem variations are discussed.