This paper worked on a newly developed Economic Production Quantity (EPQ) model when Storage capacity is limited due to high rent in super market. But model is flexible and reliable for customer for better production in mixed environment with handling the arrogant customers. The model has incorporated as random demand, an imprecise production and shortage on space with considering the production occurred is not cent percent perfect , i.e, a fraction of produced items are defective . Therefore defective items are sold at a reduced price and the selling price of fresh units is depends on our unit production cost. Model is the modified version of General Economic Ordered Quantity (EOQ) Model for instantaneous production under shortage. The model is formulated for “maximize the average profit under optimum production cost under certain constraints on invested funds”. The constraints function has been formulated with the help of concept of differential equation when initial condition and boundary values are given. Finally this model behaves like mathematical programming problems hence can be solved by geometric programming problem for optimized the Profit function to find the value of decision variables. The sensitivity of this model can be illustrated by numerical example. This is the best fit of normal distribution for optimum reliability during inventory production . Key Words: EOQ & EPQ Model, Boundary Value Problems (BVP) of Differential Equation, Mathematical Programming (MP) & Geometric Programming Problem