The responsibility in inventory models decides of how much or how many of inventory items to order. An economic order quantity (EOQ) differs from a model to another according to the assumptions and the variables. This paper has developed the EOQ in two deterministic inventory model (Purchases with shortage and production with shortage) of multi-item when the objective function is subjected to annual number of orders. The constraints are assumed to be active if the left hand side does not satisfy the right hand side condition. Thus, Lagrange method is used to find the new multi-item EOQ in each two models with the constraint to achieve the new formula of EOQ. Finally, a numerical example is provided to justify the proposed model.