Abstract: This study presents a cost optimization model for multi-item inventory system having deterministic demansd. We assume that backlogging is allowed. The maximum capacity of the inventory is assumed to be constant Qi. The total annual variable cost is derived in terms of Qi and it is a non-linear function of Qi. First the deterministic inventory problem is solved using constrained optimization technique. In addition to the above, we assume that the total expenditure and floor space are not precisely measured function. A non-linear programming problem is formulated and solved by Lagrange multiplier method. Numerical examples are provided for deterministic inventory problem to emphasize the results in crisp.