Company NEWCO produces product Z on a machine with a constant production rate P = 75 units per week. The demand for Z appears to be constant over time at a rate of 45 units per week. A fixed cost K = 5000 is incurred every time a new production run starts. The inventory holding cost for product Z is 5 per unit per week. Calculate the optimal production lot size for product Z and illustrate through a diagram how the inventory of Z evolves over time.