3. (a) An importer buys items in bulk from abroad and sells them on to the local population with a fast delivery time. They receive orders for 250 items per month. It costs 30 to have a shipment of new stock delivered, which takes 1 month to arrive after being ordered. Storing each item costs 10p per month. Find the optimal order size and order frequency for the importer to minimise their costs. Justify your answer. [3 marks] (b) The seller realises that the demand each month varies, and can be seen as normally distributed with mean 250 and variance 100. They decide to create a buffer stock such that the probability of running out of stock is at most 1%. By what percentage does this increase the importers operating costs? [7 marks]