Asupplier to toyota stamps out parts using a press. changing a part type requires the supplier to change the die on the press. this changeover currently takes four hours. the supplier estimates that each hour spent on the changeover costs $250. demand for parts is 1,000 per month. each part costs the supplier $100, and the supplier incurs an annual holding cost of 25%.a) determine the optimal production batch size for the supplier. b) toyota would like the supplier to reduce their batch size by a factor of four; that is, if the supplier currently produces q parts per batch, toyota would like them to produce q/4 parts per batch. what should the supplier do in order to achieve this result?