In this paper, we discussed the effects of discount price on demand and profit in a diminishing market. A production plan has been suggested for an imperfect production system. Here, demand is considered to be price sensitive and negative power function of the selling price. This problem is solved by optimization, using the Hessian matrix of order three. The main objective is to find the optimal expected average profit, optimal selling price, discount rate, backorder level, and lot-size. The recommendations are provided to offer a price discount for limited sale season on different occasions. A numerical example is presented to validate the model and is graphically illustrated accordingly.