This paper contains a production and inventory planning model with lot sizing in an RMG factory. This model is an example of mixed integer linear programming. The primary goal of this approach, which combines the make-to-order (MTO) and make-to-stock (MTS) production methods are to simultaneously satisfy existing customer orders and new customer orders in order to reduce the total cost. Here, make-to-order (MTO) and make-to-stock (MTS) production systems are becoming more and more common since they allow businesses to increase revenues while managing expenses by maintaining a positive cash flow. For mixed contexts where demand is cyclical but predictable, and the model stores the predicted data and fresh forthcoming orders.