need help with this

Problem 2: Inventory Management (30 points) The Officemax at Arborland sells a type of pen for $1.50 per unit. This has been a relatively popular pen, and customers have buy them at a a constant rate of 750 per week. This store orders its pens from a national supplier at a unit cost of $0.20 per pen. Management estimates that the cost of placing an order is $90 and a holding costs of $1.04 per pen per year. Officemax has a policy of not allowing backorders and management constantly monitors the inventory levels. For the purposes of this problem, assume that any order placed arrives immediately and 52 weeks per year. (a) The manager recently learned about the Economic Order Quantity (EOQ) model and wants to update the store's ordering policy. Does the manager's problem meets the assumptions of the basic EOQ model? Explain. (5 points) (b) Under the basic EOQ model, what is the manager's optimal ordering quantity? (5 points) (c) What is the optimal ordering quantity in integer units? (5 points) For parts (d) and (c), suppose that Officemax's current supplier went out of business. The manager was able to find a new supplier who would provide pens at the same unit cost of $0.20 per pen and does not offer a quantity discount. This new supplier is further away and orders now take 1 week to arrive. (d) What re-order point should the manager use to maintain the store's policy that pens will not be backordered? (5 points) (e) Now suppose that the Arborland's Officemax has updated its demand forecast to consider stochas- tic demand and determines that weekly demand is uniformly distributed from 500 pens to 1000 pens. The manager adjusts the store's policy so that backorders are allowed but wants to guar- antee with 99% probability that the store will not stock out of pens in the time between when an order is placed and when it is received. What should the new re-order point be to satisfy this service measure? Hint: the edf function of an U(a,b) is F(x) = for a