This research is directed towards the minimization of the total cost of the single-item, single-source, deterministic inventory system in the face or multiple constraints. The Lagrangian multiplier technique is used for optimization. Two models, the general model and the special model, with multiple constraints are studied. For the special model the solution becomes indeterminate and/or incompatible whenever more than one constraint is active and the trial and error method is suggested for this situation. For the general model, the constraints are classified into two basic groups of incompatible constraints. Also, other possible groups of incompatible constraints are listed. A sample solution for one group, out of many possible groups, of compatible constraints is presented. Illustrative examples are given. / Master of Science