Abstract: A deteriorating inventory model of EOQ has probabilistic and shortages. Shortages can be accepted, but it is balanced by fully backlogged. Demand considered as quadratic time function and holding cost is parabolic. Demand items considered as a quadratic with highest power coefficient has negative sign, which pursues the Beta passion.From these inferences, a mathematical model has been framed and worked out using numerical solutionwith the help of computation table and represented using graph. Here the main aim determines thetime period should be optimal, highest order quantity of very least overall average cost.