EPQ Model finance exercise question

Can someone help me with the following exercise

Consider the classic Economic Production Quanity (EPQ) model. A firm must decide the duration of production runs, given that demand for its product is constant throughout the year and shipments from the factory can be made at the firm’s discretion. The production schedule can be depicted as follows:


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Let D be the annual demand (in litres - assume the product is liquid or infinitely divisible) and T the production interval (fraction of a year, i.e., T = 0.5 means that two production runs per year are made). During the production run, the firm must pay inventory holding costs of €h per litre per unit time. Production costs are €p per litre and the firm faces an opportunity cost of r%. At the end of the production run, a shipment cost of €S is incurred. Suppose additionally that the firm allows it customers a trade credit period: specifically, it receives payment for each shipment after an interval of length t (also a fraction of a year).

Question: Show that when simple interest is used, theinterval optimal production T* (i.e., the interval that minimizes total annual costs) does not depend on the trade credit period.