A supplier 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?