please answer all the parts of this question within 30 minutes. make sure the explanation and reasons are explained in very detailed manner , Attempt the answer only if your are 100% sure that its correct. else leave it for other tutor otherwise i will give negative ratings and will also report your answer for unprofessionalism. Make sure the answer is 100% correct and is not copied from anywhere. ATTEMPT THE QUESTION ONLY IF YOU ARE 100% CORRECT AND SURE. ELSE LEAVE IT FOR ANOTHER TUTOR. BUT PLEASE DONT PUT WRONG ANSWER ELSE I WILL REPORT.

The Pizza Corporation is a fast food restaurant chain based in London that operates sixteen restaurants across the city. At the moment, each restaurant manages its inventory independently and orders supplies from the grocery wholesaler directly. The weekly demand for each of the restaurants is normally distributed with a mean of 1800 units and a standard deviation of 600 units and each unit ordered costs about 1. The fixed cost for ordering including transportation amount to 90 and the company assumes an annual inventory holding cost rate (including physical holding cost and cost of capital) of 20%. The lead time between the wholesaler and the restaurants is one week. i. Given that all restaurants manage their orders and deliveries independently, what should be their optimal order quantity when there are 50 weeks of operation a year? ii. How much inventory does the company as a whole keep on average and what are its total annual cost including the ordering and inventory holding cost? After reconsidering its operations, the Pizza Corporation aims to pool its purchasing activities at the grocery wholesaler. Instead of allowing each restaurant to order individually, orders for all restaurants will now be merged and send to the wholesaler at the same time. The wholesaler will deliver merged orders to a central restaurant at which orders are split equally and distributed across the other restaurants afterwards. Pooling of purchasing activities does not have an impact on the restaurants lead time, the fixed ordering and transportation cost, however, will increase to 360 due to the additional transportation activities required between the restaurants. iii. Given the company is managing its central supplies correctly, how does pooling of its purchasing activities influence the company's average inventory and its total annual cost including the ordering and inventory holding cost? iv. Explain the effect of pooling purchasing activities with regard to the average inventory level as well as total annual cost including the ordering and inventory holding cost. v. What else might the company do in orderto reduce the amount of inventory held