This paper describes an EOQ inventory model when deterioration rate follows Weibull distributions. It is a two way parameter distribution of demand rate and other is holding cost. Which is assumed to be function of selling price and parabolic in terms of time respectively. In this EOQ model with shortage case is taken into consideration in detail. Whenever shortage allowed is completely backlogged. To achieve the result numerical examples for both cases shortage as well as without shortage are considered. The sensitive analysis for the inventory EOQ model has been performed to study the effect of changes the variation of parameters associated with the design model.