Question 2: A logistics company is preparing to take over the supply and inventory process for one of its customers. The customer makes its plans on annual basis and has handed the following information. Once an order is placed, it takes 3 weeks to receive the order from a supplier. The aggregate demand for the product family during the lead time is 12 boxes in average. The purchasing cost of one box is $4, and the cost of placing an order is $60 for paperwork and transportation. The interest rate for holding cost is estimated at 20 percent annually. There is a substantial uncertainty in demand. The calculations show that the demand during the lead time follows a normal distribution with a standard deviation of 16 boxes. The company estimates that the loss of customer goodwill for not being able to serve the order when requested amounts to $25. Analyzing the data, the company decides to implement a (Q, R) policy to control the inventory for this product group. Determine the following quantities: a) (20 points) The optimal values of the order quantity and the reorder level. b) (20 points) The average annual cost of holding, setup, and stock-out associated with this item assuming that an optimal policy is used c) (20 points) Optimal safety stock for this order