This paper develops a linear programming model to assist in identifying a capacity feasible Master Production Schedule (MPS) in Material Requirements Planning (MRP) systems. It aims to take a more sophisticated approach than Rough Cut Capacity Planning and yet avoid the trial and error simulation of Capacity Requirements Planning. By assuming lot-for-lot production of components, the model keeps down intermediate stock levels and lead times. In addition, by preprocessing data on the end-items' component structure and the utilization of bottleneck resources over each component's production lead time, the model does not need to explicitly take the MRP explosion of components into account during optimization, thus keeping model size to manageable levels. A simple computational example is tested, showing that the rigidity of the model's lot-for-lot component production can be counterbalanced by the judicious use of overtime as identified by a simple extension of the model.