This paper presents an integrated production and inventory model. Our multi-echelon model includes the maximization of production while it minimizes the cost of production, inventory holding and setup operations. The model consists of two main parts, the primary and finishing operations. The primary operation corresponds to purchasing of raw material and the finishing operation is for preparation of finished product. Demand is influenced by price elasticity and the cost of purchasing raw material is also affected by demand. The resulted model, therefore, is highly nonlinear and non-convex. Geometric Programming (GP) is used to locate the global solution of the proposed model. We analyze the solution in different cases in order to study the behaviour of the model and for each case, a numerical examples is used to demonstrate the implementation of our analysis.